Common Logarithms

Unlocking the Power of Logarithms

Discover the incredible potential of logarithms and how they can be used to solve complex mathematical problems. Explore the fundamental concepts and applications of logarithms in various fields such as science, engineering, and finance. Unlock the power of logarithms and enhance your problem-solving skills.

Introduction to Logarithms

• Logarithms are mathematical functions that help solve exponential equations.
• They are the inverse of exponentiation.
• Logarithms have various applications in science, engineering, and finance.
• Common logarithms use base 10, while natural logarithms use base e.
• Logarithms can simplify complex calculations and help analyze data.

Multiple Choice

What are the applications of logarithms?

• Solving exponential equations

• Analyzing data

• Simplifying complex calculations

• All of the above

Applications of Logarithms

• Solving exponential equations: Logarithms are used to solve equations where the variable is in the exponent.
• Analyzing data: Logarithms help in analyzing data that spans a wide range of values.
• Simplifying complex calculations: Logarithms simplify calculations involving large numbers or complex operations.

The base of the log is 10 and the base of the the exponent is also 10.

Multiple Choice

Rewrite the equation in logarithmic form.

• A
• B
• C
• D

Multiple Choice

Rewrite the equation in logarithmic form.

• A
• B
• C
• D

Multiple Choice

Rewrite the equation in logarithmic form.

• A
• B
• C
• D

Multiple Choice

Rewrite in exponential form.

• A
• B
• C
• D

Multiple Choice

Rewrite in exponential form.

• A
• B
• C
• D

Multiple Choice

To evaluate a logarithm statement log₉81, you think "9 to what power is 81".

• True, and it's 2

• False

Multiple Choice

Condense the Logarithm $$5\log_{ }a\ -\ 25\log_{ }b$$  

• $$\log\ \left(a^5+b^{25}\right)$$  

• $$\log\ \left(a^5-b^{25}\right)$$  

• $$\log\ \left(ab\right)^{25}$$  

• $$\log_{ }\ \left(\frac{a^5}{b^{25}}\right)$$  

Multiple Choice

Condense $$3\log_{ }x+4\log_{ }y\ +\log_{ }z$$  

• $$\log_{ }\ x^3y^4z$$  

• $$12\log_{ }\ xyz$$  

• $$\log_{ }\ 3x4yz$$  

• logx³y³z³

Multiple Choice

Condense the Logarithm $$5\log_{ }a\ -\ 25\log_{ }b$$  

• $$\log\ \left(a^5+b^{25}\right)$$  

• $$\log\ \left(a^5-b^{25}\right)$$  

• $$\log\ \left(ab\right)^{25}$$  

• $$\log_{ }\ \left(\frac{a^5}{b^{25}}\right)$$  

Multiple Choice

Condense $$3\log_{ }x+4\log_{ }y\ +\log_{ }z$$  

• $$\log_{ }\ x^3y^4z$$  

• $$12\log_{ }\ xyz$$  

• $$\log_{ }\ 3x4yz$$  

• logx³y³z³

Multiple Choice

Use the change-of-base formula to evaluate $$\log_211$$  

• $$3.459$$  

• $$4.359$$  

• $$5.123$$  

• 2.345

Multiple Choice

Simplify: $$\log_4\left(x+4\right)-\log_4\left(x-5\right)$$  

• $$\log_49$$  

• $$\log_4\left(2x-1\right)$$  

• $$\log_4\left(x^2-x-20\right)$$  

• $$\log_4\left(\frac{x+4}{x-5}\right)$$  

Multiple Choice

Simplify: $$2\log_3\left(11x\right)$$  

• $$\log_3\left(22x\right)$$  

• $$\log_3\left(121x\right)$$  

• $$\log_3\left(121x^2\right)$$  

• $$\log_3\left(11x^2\right)$$  

Multiple Choice

Simplify: $$\frac{1}{4}\log_516+3\log_5x$$  

• $$\log_5\left(4x^3\right)$$  

• $$\log_5\left(2x^3\right)$$  

• $$\log_5\left(6x\right)$$  

• $$\log_5\left(\frac{2}{x^3}\right)$$  

Multiple Choice

Simplify: $$\frac{1}{4}\log_281+\frac{1}{2}\log_249$$  

• $$\log_221$$  

• $$\log_210$$  

• $$\log_2\left(\frac{3}{7}\right)$$  

• $$\log_244.75$$  

Multiple Choice

Simplify: $$\frac{1}{2}\log_964+\log_9x$$  

• $$\log_9\left(32x\right)$$  

• $$\log_9\left(8x\right)$$  

• $$\log_9\left(\frac{8}{x}\right)$$  

• $$\log_98x$$   

Multiple Choice

Write the expression as a single logarithm.   Then simplify if possible.
log 6 - log 3 + 2 log 7

• log 98
• log 78
• log 56
• log 45

Multiple Choice

Expand using the properties of Logaritms $$\log_{ }\ \frac{x^3}{y^4z}$$  

• $$\log_{ }x+4\log_{ }y\ +\log_{ }z$$  

• $$3\log_{ }x-4\log_{ }y\ -\log_{ }z$$  

• $$3\log_{ }x+4\log_{ }y\ +\log_{ }z$$  

• $$3\log_{ }x-4\log_{ }y\ +\log_{ }z$$  

Multiple Choice

Use these and other properties of logarithms to evaluate the expression.

$$\log_232\ -\ 6^{\log_63}$$  

• $$2$$  

• $$-2$$  

• $$8$$  

• $$3$$  

Multiple Choice

Expand the logarithm.
$$\log_4\sqrt{x^3y}$$  

• $$\frac{1}{2}\log_4\left(x\right)-\frac{1}{2}\log_4\left(y\right)$$  

• $$\frac{3}{2}\log_4\left(x\right)-\frac{1}{2}\log_4\left(y\right)$$  

• $$\frac{1}{2}\log_4\left(x\right)-\log_4\left(y\right)$$  

• $$\frac{3}{2}\log_4\left(x\right)-\log_4\left(y\right)$$  

Multiple Choice

Use the change-of-base formula to evaluate $$\log_7\ \frac{3}{16}$$  rounded to two decimal places

• $$0.82$$  

• $$0.86$$  

• $$0.85$$  

• $$0.87$$  

Multiple Choice

Expand the logarithm.
$$\log\frac{x}{y^6}$$  

• $$\log x+6\log y$$  
  

• $$\log x-6\log y$$  
  

• $$\log x+\log6y$$  
  

• $$\log x-\log6y$$  
  

Multiple Choice

Expand . $$\log_6\left(\frac{5x^3}{y}\right)$$  

• $$\log_65x^3-\log_6y$$  

• $$\log_65+\log_6x^3-\log_6y$$  

• $$\log_65+3\log_6x-\log_6y$$  

• $$\log_65+3\log_6x+\log_6y$$  

Multiple Choice

Evaluate $$\log_52+\log_520-\log_54$$  . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

• $$1.4307$$  

• $$-1.4307$$  

• $$1.3470$$  

• $$-1.347$$  

Multiple Choice

Evaluate $$\log_6\ \frac{1}{36}+\log_636-5^{\log_61}$$  . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

• $$1$$  

• $$5$$  

• $$12$$  

• $$0$$  

Multiple Choice

Evaluate $$\log_6\ \frac{1}{216}+\log_24+\log_2\ \frac{1}{8}$$  . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

• $$4$$  

• $$-4$$  

• $$2$$  

• $$5$$  

Multiple Choice

Evaluate $$\log_330-\log_4\ 4^5$$  . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

• $$1.9041$$  

• $$-1.9041$$  

• $$19,041$$  

• $$9,041$$  

Multiple Choice

Evaluate $$1000^{\log_{10}4}-\log_464+25^{\log_510}$$  . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

• $$161$$  

• $$61$$  

• $$-161$$  

• $$126$$