SOLUTION: {{{ log3(n^2-5)^4=4 }}} I think this is how you start log base3(n^2-5)^4=3^4 (n^2-5)^4=81

Question 281204:
I think this is how you start
log base3(n^2-5)^4=3^4
(n^2-5)^4=81
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
>I think this is how you start
>log base3(n^2-5)^4=3^4

Actually the logarithm should be gone when you rewrite the equation in exponential form:

At this point, one way to solve the equation is to find the 4th root of each side:

Since 4th roots can be positive or negative we must account for both:
or
These are quadratic equations so we want one side equal to zero:
or
These will not factor. So we'll use the Quadratic equation on each. We should end up with:
or or or

When solving logarithmic equations you should check your answers. You must make sure no arguments of any logarithms are zero or negative.

Checking :

Check!

Checking :

Check!

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