Re-writing exponentials as Logs. HELP!

Question

How do I write y=a(b)^x in Logarithmic form? I know how to convert it from y=b^x form but I don't know what "to do" with the variable 'a', The function I want to convert is: y=0.02(1.001)^x

 

Answer 1

The first answer will definitely allow you to solve the exponential function listed for x.  To be even more precise (about the logarithmic form), when you convert an exponential function into logarithmic form you typically would express the logarithm in terms of the original base, b, vice the combination of base 10 and base b.

 

For example

 

y=ab^x

y/a=b^x

 

converts to

log_b(y/a)=log_b(b^x)

log_b(y/a)=x

 

Or x=log_by-log_ba

 

Note the original answer can be manipulated (using the change of base property) to arrive at the result I just stated.

 

Also, the form in the original answer might be easier to use if your calculator only does log₁₀ (ie the normal log button).

 

Good Luck

 

Cheers

 

-Chris

 

Answer 2

Divide both sides of the equation by a.

 

y / a = b^x

 

 

Now log both sides of the equation and bring any exponents as the coefficient of log.

 

log(y / a) = xlog(b)

 

 

(logy - loga) / logb = x