Question

which logarithmic equation correctly rewrites this exponential equation? 8^x=64

Answer 1

which logarithmic equation correctly rewrites this exponential equation? 8^x=64​

we have that

64=2^6

so

substitute

8^x=2^6

8=2^3

so

(2^3)^x=2^6

2^(3x)=2^6

therefore

3x=6

x=2

with log

apply log both sides

log(8^x)=log(64​)

apply property of log

x*log(8)=log(64)

x=log(64)/log(8)

simplify

x=log(2^6)/log(2^3)

x={6log(2)}/{3log(2)}

x=6/3

x=2