MATH IV FOUNDATIONS Q2 TEST 1 LOGARITHMS

The common logarithm has what base?

• 10
• 0
• e
• -e

Log with a base "e" (log_e) is the same thing as...

• "e"
• Natural Logarithm (LN)
• Common Logarithm (Log)
• Natural Log, base "e"
  LN_e

Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions 

Approximate the value to the nearest ten-thousandths using the change of base formula. log₂35

• 1.5592

• 5.9187

• 5.1293

• 1.8990

Rewrite log₂8 = 3 in exponential form

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

Choose the correct expanded common logarithm:

 $\log\left(\frac{m^3}{n}\right)$  

•  $\log m-\log3-\log n$  

•  $3\log m+\log n$  

•  $3\log m-\log n$  

•  $3\log(m-n)$  

Choose the correct expanded common logarithm:

 $\log(xy^2)$  

•  $\log x+2\log y$  

•  $\log x+\log y^2$  

•  $\log x-2\log y$  

•  $\log x+\log y+\log2$  

Expand the logarithm expression

log 5x/4y

• log 5x + log 4y

• log 5x - 4log y

• (log 5 + log x) - (log 4 + logy)

• 5log x - 4 logy

True or False

 $\ln\left(x+3\right)-\ln\left(2x\right)=\frac{\ln\left(x+3\right)}{\ln\left(2x\right)}$  

• True, subtraction between two logarithms is division in condensed form.

• True, a logarithm is an exponent. When dividing like bases you subtract exponents therefor dividing logarithms as in this example.

• False, subtraction between two logarithms is division within a single logarithm in condensed form.

Solve for x:

log₂(x+3)=4

• 16

• 13

• 3

• 10