Math exam tomorrow...how do you solve this?

Question

3^(4x+1) = 81
answer: 3/4

but how would u do it with logarithms cuz i have more liek it u cant do like that

Answer 1

You could use logarithms, but there's an easier way. Note that 81 is a power of 3 - it's 3^4. So:

3^(4x + 1) = 3^4

If the bases are equal, then the exponents must be equal as well, so

4x + 1 = 4
4x = 3

x = 3/4

Edit: OK. Logarithms are exponents. I'm going to assume we're using base 10 logs. Given that, there's a basic equation:

log (x^y) = y log x

The log brings the exponent down in front as a multiplier.

So, in this problem:

3^(4x + 1) = 81

log 3^(4x + 1) = log 81

(4x + 1) log 3 = log 81

4x + 1 = (log 81)/(log 3)

4x = (log 81)/(log 3) - 1

x = [(log 81)/(log 3) - 1]/4

And I promise you - if you plug that into a calculator correctly, you'll get 3/4.

Do go back and look at your problems again. If you're only in algebra I, it's very possible that they can all be worked the way I did the first one.