Question

What equation is equivalent to 2^3^x =10

Answer 1

`log_2(10)`

how to find

Simplify the equation using logarithms.

part 1

`2^3x=10`

`log_1_0(2^3x)=log_1_0(10)`

log rule ⇩

`log_a(x^y)=y*log_a(x)`

move exponent out of log.

`x*log_1_0(2)=log_1_0(10)`

part 2

isolate variable further

`x*log_1_0(2)=log_1_0(10)`

`x=(log_(10)(10))/(log_(10)(2))`

formula for combining logs. ⇩

`\frac {log_b(x)}{log_b(a)}=log_a(x)`

the result ⇩

`x=log_2(10)`