Logarithm help?

Question

I have two questions.

The first is 24=e(x+1).....where x+1 is an exponent. I know its very simple but i just can't remember how to solve it.

The second is log(4)x=3/2....where 4 is the subscript.

Any suggestions would be helpful.

Answer 1

Take ln() of both sides. Then

ln(24) = x + 1
-> x = ln(24) - 1

For second question

4^[log(4)x] = 4^(3/2)
x = [4^(1/2)]^3 = 8

Answer 2

Hi,
What you want to do is get rid of the e, and you can do that by taking the natural log of both sides. Remember that ln (e^x) = x.
So,
ln 24 = ln (e^(x+1))
ln 24 = x+1
-1 + ln 24 = x (We sometime write it this way to avoid confusion.)
-1 + 3.178 = x
2.178 = x

Now, for the second one:
Convert this to an exponential:
Remember, that a logarithm is the exponent we raise the base to in order to get the argument (number, in your case x).
So, we convert this problem to an exponential using that information.
log(base 4) x = 3/2
4^(3/2) = x (Raise the base to the exponent (logarithm).
8 = x
You can do this last step on your calculator by entering:
4^(3/2)

Hope this helps.
FE