ARewrite the following exponential equation as an equivalent

A.Rewrite the following exponential equation as an equivalent logarithmic equation.

37⁷ = x

B.Find the exact value of the following:   log 8 ( 1 64 )   

c.What is the domain of the following function?

D.Solve the following equation for x:

log6x=3

f(x)=log15(164x)

Solution

A. 377=x

377¹=x

log₃₇₇x=1

B.log₈(1/64) = log₈8^-2 =-2 log₈8 =-2

C. f(x)=log₁₅(16-4x)

Log cant take negative values or zero

16-4x>0

x<4

Domain is (-infinity,4)