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,