help

Solve for x over the real numbers:
4^(log(x)/log(7)) = 16

Take the logarithm base 4 of both sides:
log(x)/log(7) = 2

Multiply both sides by log(7):
log(x) = 2 log(7)

2 log(7) = log(7^2) = log(49):
log(x) = log(49)

Cancel logarithms by taking exp of both sides:
x = 49

Here's a slightly shorter approach

Note that 4^2  = 16

Which must mean that

log ₇ x  =  2

So....in exponential form    7^2  = x   =  49