Review for Logarithms Quiz

Presentation

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Mathematics

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10th - 12th Grade

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Practice Problem

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Medium

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CCSS

HSF.BF.B.5, HSF-BF.B.4A, HSF-IF.C.7E

Standards-aligned

Tia BOLSA)

Used 17+ times

FREE Resource

6 Slides • 10 Questions

Review for Logarithms Quiz

Switching from Logarithmic Form to Exponential form $\log_bx=y\ \ \leftrightarrow\ \ b^y=x$

$\log_39=2\ \ \leftrightarrow\ \ 3^2=9$

Multiple Select

Write the logarithm in exponential form: $\log_381=4$

$3^4=81$

$4^3=81$

Multiple Select

Write the logarithm in exponential form: $\log_28=3$

$2^8=3$

$2^3=8$

What does a logarithm mean? $\log_bx=y$

"How many times do we multiply b to get x ? We multiply b "y-times" to get x."

Multiple Choice

Evaluate: $\log_864=$

Multiple Choice

Evaluate: $\log_5125=$

A logarithmic function is the inverse of an exponential function.

Proof:

$\log_bx=y$

Switch x and y

\log_by=x

Solve for y by rewriting in exponential form

b^x=y

Therefore, the inverse of

\log_bx=y

b^x=y

Multiple Choice

Write the inverse function of: $\log_5x=y$

$5^x=y$

$x^5=y$

Multiple Choice

Write the inverse function of: $\log_9x=y$

$x^9=y$

$9^x=y$

Change of base formula

\log_bm=\frac{\log m}{\log b}

(base b goes in the basement)

Multiple Choice

Write logarithm in exact form by using the change of base formula:
$\log_47$

$\frac{\log7}{\log4}$

$\frac{\log4}{\log7}$

Multiple Choice

Write logarithm in exact form by using the change of base formula:
$\log_{34}17$

$\frac{\log34}{\log17}$

$\frac{\log17}{\log34}$

Graphing $y=\log_bx$

The graph of $y=\log_bx$ is obtained by reflecting $y=b^x$ across the $y=x$ line.

Domain: $x>0$ (you cannot take the log of 0 or negative numbers)
Range: All real numbers / $\left(-\infty,\infty\right)$

Fill in the Blanks

What is the DOMAIN of a logarithmic function?

Type answer...

Fill in the Blanks

What is the RANGE of a logarithmic function?

Type answer...

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