2. 1. Solve using logarithms, round to the nearest thousandth.
3*5ⁿ+⁷+5=38
• To begin this problem, you have to get the exponent by itself. You do
this by subtracting the 5 from each side, and dividing each side by 3.
Like this: 3*5ⁿ+⁷+5=38 this leaves you with 3*5ⁿ+⁷=33
-5 -5 now you divide 3 3
• Now that the exponent is by itself 5ⁿ+⁷=11 you can solve by using
a logarithm, which is the inverse of an exponent. The inverse undos
the original function, helping to get n by itself
log₅11=n+7
• You can now figure out the log₅11 because it is just a number:
1.489896=n+7 to get n by itself all you have to do is subtract
7 -7 -7 from both sides and then you have the
answer
• n=-5.510