Converting Exponential and Logarithmic Equations

Logarithmic and Exponential Conversions

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Poll

Did you know that Logarithms are really Exponents?

Pay attention to the placement of the a, b, and c. Move forward to watch a video of some examples.

Logarithmic & Exponential Conversions

Watch video and move forward to answer quiz questions.

Multiple Choice

Using the equation below, which value becomes the BASE of the logarithm?

$$7^x=1.2$$  

• 1.2

• x

• 7

• 10

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81

• log₈₁3 = 4

• log₃81 = 4

• log₄81 = 3

Multiple Choice

Rewrite 7^x = 13 in logarithmic form.

• log ₇ x = 13

• log ₁₃ x = 7

• log ₇ 13 = x

• log _x 7 = 13

Multiple Choice

Rewrite 4^-2 = 1/16 in logarithmic form.

• log ₄ (1/16) = -2

• log _-2 (1/16) = 4

• log ₄ (-2) = 1/16

• log _1/16 (4) = -2

Multiple Choice

Write b^k = m into logarithmic form.

• log _b m = k

• log _m k = b

• log _b k = m

• log _k m = b

Multiple Choice

Rewrite in log form: $$8^{-3}=\frac{1}{512}$$  

• $$\log_8\left(-3\right)=\frac{1}{512}$$  

• $$\log_8\ \frac{1}{512}=-3$$  

• $$\log_{-3}8=\frac{1}{512}$$  

• $$\log_{\frac{1}{512}}8=-3$$  

Multiple Choice

Change to Exponential Form:

log₆36 = 2

• 2⁶=36

• 6²=36

• 36²=6

• 36⁶=2

Multiple Choice

Rewrite log_pt = m in exponential form.

• p^t = m

• t^m = p

• m^t = p

• p^m = t

Multiple Choice

Rewrite in exponential form: $$\log_4\ \frac{1}{64}=-3$$  

• $$\left(\frac{1}{64}\right)^{-3}=4$$  

• $$4^{\frac{1}{64}}=-3$$  

• $$\left(-3\right)^4=\frac{1}{64}$$  

• $$4^{-3}=\frac{1}{64}$$  

Multiple Choice

$$\log_6\frac{\text{1}}{\text{36}}=-2$$  Write in exponential form.

• $$\frac{6}{36}=-2$$  

• $$36^{-2}=\frac{1}{6}$$  

• $$6^{-2}=\frac{1}{\text{36}}$$  

• $$36^6=-2$$  

Multiple Choice

Write log ₂₅ 5 = 1/2 in exponential form.

• 25⁵ = 1/2

• 25^1/2 = 5

• 5²⁵ = 1/2

• 5^1/2 = 25