Question

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

Answer 1

Answer:

$log_2(10)$

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

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

$x=\frac{log_{10}(10)}{log_{10}(2)}$

formula for combining logs. ⇩

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

the result ⇩

$x=log_2(10)$