Math Help With Exponents

March 1st, 2011

$math help with exponents$
Question: I need Help With Math! exponents and logarithms?

36^x – 26*(6^x) = -105

I know that you convert the 36 to 6^2, which would then be

6^2x – 26*(6^x) = -105

but that’s all I’ve got!! thanks for any help.

Answer: 36^x – 26*(6^x) = -105

(6^x)^2 – 26(6^x) + 105 = 0

Now put 6^x = u:
u^2 – 26u + 105 = 0

That’s a plain quadratic in u.
(u – 21)(u – 5) = 0
u = 21 or u = 5

Case 1 (u = 21):
6^x = 21
x log(6) = log(21)
x = log(21) / log(6).

Case 2 (u = 5):
6^x = 5
x log(6) = log(5)
x = log(5) / log(6).

Math Help Exponents 4: Division

Math Help