Solving Logarithms and Change of Base

Rewrite log_x95 = 2.3

• x^2.3 = 95

• 95^2.3 = x

• 2.3⁹⁵ = x

• x⁹⁵ = 2.3

Rewrite 1.6^(x+2) = 14.1

• log_1.614.1 = x+2

• log_1.6(x+2) = 14.1

• log_14.1(x+2) = 1.6

• log_(x+2)1.6 = 14.1

Which of the following has a domain of all real numbers, x > 2 ?

• y = log₂ x

• y = log₃ (x+2)

• y = log₄ (x - 2)

• y = log₇ x - 2

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

• log₂(x/y⁵)

• log₂(xy⁵)

• log₂(x/y)⁵

• log₂(x/5y)

Solve for x:  log₆x + log₆(x-5) = 2

• √7

• 9

• 4

• none of these

ln(x+8) - ln (8) = 3

(you're going to need a calculator and to "e" to the power of something)

• 152.68

• 188.77

• 4.24

• 8.01

log₉(x)+log₉(x+2)=log₉(35)

• 5

• 7

• -5

• -13

log7+log(x²-4)=log35

• -1

• -2

• -3

• -4

Write as one logarithm. Simplify, if possible.
log₅125 - log₅25

• 1

• 0

• 5

• -1

log₂(x+3)=4

• 16

• 13

• 3

• 10