Hello from MrBillDoesMath!
Answer: x = (log (d/a)) / log(b)
Discussion:
Take the logarithm of both sides of the equation:
log (a * b^x) = log(d)
Logarithm of a product is the sum of the logs. Apply this to the left hand side:
log(a) + log(b^x) = log(d)
The logarithm of an exponent is equivalent to the exponent times the log of the base:
log(a) + x * log(b) = log(d)
Subtract log(a) from each side:
x * log(b) = log(d) -log(a)
Dividing both sides by log(b) gives
x= (log(d) - log(a))/ log(b) or more simply
x = (log (d/a)) / log(b)
Thank you,
MrB
