I don't know how to isolate an exponent with a variable and a known number, e.g. [math]2 = 3^{0.01t}[/math]. How do I isolate the term 't'?

 

I know that you can square root the opposite side to remove the exponential, like this: [math]\sqrt[0.01t]{2}=3[/math]. But that still doesn't solve the isolation of the term 't'.

 

Any help??

You can use natural logs to work this out quickly. First take the natural log of both sides and get [math]\ln{2}=\ln{3^{0.01t}}[/math] This can be rewritten as [math]\ln{2}=0.01t\ln{3}[/math], so [math]t=100\frac{\ln{2}}{\ln{3}}[/math]

Yeah I figured that I ought to use Natural logs, and I got a different isolation of t. I got [math]t = \frac{In2}{0.01In3}[/math]. How did you get the 100? I calculated Ducky Havok's method, and I got the same answer. Just to my curiousity, how do you know that the 100 will work?