Simplifying and Solving Logarithm

To solve, 16^5x = 64^x+7, what would be the correct set-up?

There is more than one correct answer.

• 4^4(5x)=4^16(x+7)

• 8^2(5x)=8^8(x+7)

• 4^2(5x)=4^3(x+7)

• 2^4(5x)=2^6(x+7)

Solve:

log₂(x + 3)=5

• x=2

• x=29

• x=7

• x=32

Determine the correct set-up for:

log₄(x-1) - log₄(x+7) = log₄6

• log₄(x-1)/(x+7)=log₄(6)

• log₄(x-1)(x+7)=log₄(6)

• log₄(x+7)/(x-1)=log₄(6)

• (x-1)(x+7)=6

Solve

• A
• B
• C
• D

log₅(4x-7)=log₅(x+5)

• 3
• 12
• 4
• 7

log₂(x+3)=4

• 16

• 13

• 3

• 10

Rewrite in logarithmic form.

8^m-7 = 92

• 8⁹² = m - 7

• 92 = 8(m - 7)

• log₈92 = m - 7

• log_(m-7)92 = 8

Condense

• A
• B
• C
• D

Use multiple log properties to write as a sum or difference of two logs: log(4x³) 

• log 4 + 3log x
• 3log 4 + 3log x
• 3log 4 + log x
• log 12 + log x

Use multiple log properties to write as a single log:
log₂x -  5log₂y

• log₂(x/y⁵)
• log₂(xy⁵)
• log₂(x/y)⁵
• log₂(x/5y)