What happens when you log transform the dependent data in an exponential growth curve?

The obtained transformed data will show a linear relation when you graph log(y) vs x

This is the mathematical demonstration:

Exponential function: y= A (B)^x
log(y) = log A + x log B
log(y) = log A + (logB)x

log A is a constant and is the vertical axis-intercept
logB is a constant and is the slope of the graph
x is the independent variable

log A is a constant,