Answer:
[tex]x=\frac{log 64}{log 4}[/tex]
Step-by-step explanation:
Given the exponential equation 4^x = 64
To convert exponential equation into log equation we use the rule
b^x = a then log_b(a)=x
the base of exponent becomes the base of log equation
4^x = 64 becoes
[tex]log_4(64) = x[/tex]
WE need log with base 10, but we got log with base 4
USe change of base formula to get base 10
log_b(a)= log(a)/ log(b)
[tex]\frac{log 64}{log 4} = x[/tex]
[tex]x=\frac{log 64}{log 4}[/tex] has log with base 10
