Exponents and Logarithms

Question

I'm lost on how to solve this for z. Can anyone help?

$\left(7^\left(-2z\right)\right)^\left(7-z\right) = 49^\left(-12\right)$

score 5 · Accepted Answer · answered Feb 16 '11 at 01:00

5

The equation is equivalent to $7^{(-2x)(7-x)}=7^{2\cdot(-12)}$.

answered Feb 16 '11 at 01:00

lhf

score 2 · Answer 2 · answered Feb 16 '11 at 00:52

2

Take $\log_{7}$ of both sides and then simplify.

answered Feb 16 '11 at 00:52

NebulousReveal

score 2 · Answer 3 · answered Feb 16 '11 at 00:53

2

Write $7^{-2z}$ as $(7^2)^{-z} = 49^{-z}$

answered Feb 16 '11 at 00:53

3 Answers3