Question

how would i solve this problem using log base 10

Answer 1

First isolate the power of 10 on the right side by dividing both sides by 5:

$100=5\cdot10^{0.3t}\implies20=10^{0.3t}$

Now you're free to take the logarithm and simplify where you can:

$\log_{10}20=\log_{10}10^{0.3t}=0.3t\log_{10}10=0.3t$

Then solve for $t$:

$t=\dfrac{\log_{10}20}{0.3}\approx4.34$