Log Expressions & "Easy" Log Equations

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Watch this short video & take notes to review expanding logs.​

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​Expanding Logarithms Review

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Multiple Choice

Expand: $$\log\sqrt[3]{3ab^5}$$  

• $$\frac{1}{3}\left[\log3+\log a+5\log b\right]$$  

• $$\frac{1}{3}\left[\log3+\log a+\log b^5\right]$$  

• $$3\left[\log3+\log a+\log5b\right]$$  

• $$\left(\log3+\log a+5\log b\right)^{\frac{1}{3}}$$  

Multiple Choice

Expand: $$\ln\ \frac{4x^3}{\sqrt[]{y}}$$  

• $$\ln4+\ln x^3-\ln\sqrt[]{y}$$  

• $$\ln4+3\ln x-\frac{1}{2}\ln y$$  

• $$3\left(\ln4+\ln x\right)-\frac{1}{2}\ln y$$  

• $$\ln4x^3-\ln y^{\frac{1}{2}}$$  

Multiple Choice

Expand: $$\log_3\ \frac{2x-3}{x^5}$$  

• $$\log_3\left(2x-3\right)+5\log_3\ x$$  

• $$\log_3\ 2x\ -\ \log_3\ \left(-3\right)-\log_3\ x^5$$  

• $$\log_3\ \left(2x-3\right)-5\log\ x$$  

• $$5\log_3\ x-\log_3\ \left(\frac{2x}{3}\right)$$  

​Condensing Logarithms Review

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Watch this short video & take notes to review expanding logs.​

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Draw

Condense: 2 ln 4 + 3 ln x + 1/2 ln y

Draw

Condense: 3 ( log 5 + log n ) - 2 log m

Draw

Condense: $$3\log_5\ a\ -\ 4\log_5\ b\ +5\ \log_5\ c$$  

Please take notes in your class notes on Case 1​.

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​Solving Log Equations

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Multiple Choice

Solve the log equation: log x + log 5 = log 3 + log (x+2)

• x = -3

• x = 3

• x = -2

• x = 2

Multiple Choice

Solve the log equation: ln (x-4) - ln (x+1) = ln 6

• x = -2

• x = 5

• x = 3

• No solution.

Draw

Solve the equation. Be sure to show all work.

2 log n = log 256

Draw

Solve the equation. Be sure to show your work.

ln (x - 4) + ln 3 = ln (2x - 5)

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Take notes on your class notes for Case 2.​

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​Some text here about the topic of discussion.

​Solving Exponential Equations

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Multiple Choice

Solve the exponential equation: $$3^{\left(x-2\right)}=9^{\left(x+4\right)}$$  

• x = -10

• No solution

• x = -7

• x = 8

Multiple Choice

Solve the exponential equation: $$7^{\left(\frac{x-2}{6}\right)}=\sqrt[]{7}$$  

• x = 14

• x = 5

• x = -2

• x = -4

Draw

Solve the equation. Be sure to show your work.

$$2^{\left(2x-1\right)}=32$$  

Draw

Solve the equation. Be sure to show your work.

$$3^{\left(1-x\right)}=\frac{1}{27}$$