Question

Solve logv(x - 1) 16 = 4?

Answer 1

\[\log _{x-1} 16=4\]

Answer 2

Remember this one thing about logs: The log is the exponent.

Answer 3

So when it says log_3(z)=x it is telling you that the exponent is x

Answer 4

In your case it says the exponent is 4.
So you need to ask yourself, "What is the base?" Then write that expression with the base x-1 and the exponent 4 and it is equal to 16

Answer 5

so then the expression becomes \[(x-1)^{4}=4^{2}\] right?

Answer 6

Yes or instead of 4^2 you could put 2^4

Answer 7

\[(x-1)^4=2^4\]

Answer 8

okay, so then i would have to multiply (x-1) and 2 right?

Answer 9

Notice that the expressions are equal (you can tell that by the equal sign between them) and the exponents are the same. The only way that can be true is that the bases are also the same. So write x-1=2 and solve.

Answer 10

so x=3

Answer 11

Yes. Check it out in the original equation.

Answer 12

If the base is 2 and the exponent is 4 that does equal 16. Do you see?

Answer 13

yes, thanks!