isolate a term

[EvoN1020v]

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??

[Ducky Havok]

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]

[EvoN1020v]

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?