Exponential and Logarithms

Multiple Choice

When solving exponential equations, you must first get like _______?

• Bases

• Exponents

Multiple Choice

To solve for 196 = 14^x, what base and exponent can you re-write 196 as?

• 7²

• 14³

• 14²

• 7³

Multiple Choice

Convert this equation 19⁸ = x, to Logarithmic Form. 

• Log₈x = 19

• Log_x19 = 8

• Log₈x = 19

• Log₁₉x = 8

Multiple Choice

To solve for 343 = 7^x, what base and exponent can you re-write 343 as?

• 7²

• 14³

• 14²

• 7³

Multiple Choice

Logarithm with a base "e" (log_e) is the same thing as?

• "e"

• Natural Logarithm (LN)

• "10"

• Common Logarithm (Log)

Multiple Choice

Simplify this logarithm: 2log₃ (x+32) - 5log₃ (x-54)

• log₃ (((x+32)²)/((x-54)⁵))

• log₃ (2(x+32))/5(x-54))

• log₃ (((x+32)²) * (x-54)⁵))

• log₃ (2(x+32)) * 5(x-54))

Fill in the Blank

9^3x = 1/9, find x.

(Your answer should be in fractions)

(x=___)

Fill in the Blank

4 (18^2x-6) = 1296, find x.

(Your answer should be x=___)

Fill in the Blank

10^2x-6=32, find x.

(Your answer should be in 2 decimal points)

(x=___)

Multiple Choice

Expand this logarithm:  $$\log_5\sqrt[4]{12x^3y}$$  .

• ⅕ ( log₅12 + 3log₅x + log₅y )

• ⅕  ( log₅12 - 3log₅x - log₅y )

• ¼ ( log₅12 - 3log₅x - log₅y )

• ¼ ( log₅12 + 3log₅x + log₅y )

Fill in the Blank

log x = 2

(If your answer has a decimal, use 2 decimals points)

(x=___)

Fill in the Blank

8ln (4x-2) +6 = 22

(If your answer has a decimal, use 2 decimals points)

(x=___)

Fill in the Blank

log₇ (x² + 3x + 9) = 2

(Your answer should be ___ and  ___)

Fill in the Blank

ln_ex = 7

(If your answer has a decimal, use 2 decimals points)

(x=___)

Fill in the Blank

log₃ (log₂x) = 2

(If your answer has a decimal, use 2 decimals points)

(x=___)