Question

solve for x?

6^-x-2=13^-8x

Answer 1

take log on both sides,

Answer 2

$6^{-x-2}=13^{-8x}$ ?

Answer 3

yes

Answer 4

\[6^{-x-2}=13^{-8x}\]

Answer 5

right

Answer 6

\[\log_{10}{6^{-x-2}}= \log_{10}{13^{-8x\
[\rightarrow x = (-2\log_{10}{6} )/(\log_{10}{6}-8\log_{10}{} )\]}}\]

Answer 7

\[6^{-x-2}=13^{-8x}\implies (x+2)\ln(6)=8xln(13)\implies 8x \ln(13)-x \ln(6)=2 \ln(6)\]\[=x(8 \ln(13)- \ln(6))=2 \ln(6)\implies x=\frac{2 \ln(6)}{8 \ln(13)- \ln(6)}\]

Answer 8

the same log 10 or log e

Answer 9

Pretty cool, no?

Answer 10

ok, cool

Answer 11

Yours was perfectly correct, but I thought maybe somebody would benefit from a little more detail.

Answer 12

yea, i expalin no detail