Solve for x. 5^(-x-3) =8^(5x) Write the exact answer using base-10 logarithms.

Question

Solve for x.


`5^(-x-3) =8^(5x)`
Write the exact answer using base-10 logarithms.

Answer 1

`5^((-x-3))=8^(5x) \implies \\5^((-x-3))=8^(5x) \implies \\\log5^((-x-3))=\log{8^(5x)} \implies \\(-x-3)\log{5}=5x\log{8} \implies \\-x\log{5}-3\log{5}=5x\log{8}\implies \\-x\log{5}-5x\log{8}=3\log{5}\implies \\ -x(\log{5}+5\log{8}})=3\log{5} \implies \\-x=\frac{3\log{5}}{\log{5}+5\log{8}}\implies \\x=\frac{-3\log{5}}{\log{5}+5\log{8}}`

Answer 2

Hello,

`5^(-x-3)=8^(5x)\\\Rightarrow\ (-x-3)\ Log(5)=5x\ Log(8)\\\Rightarrow\ -xLog(5)-3Log(5)=5x Log(8)\\ \Rightarrow\ x(5 Log(8)+Log(5))=-3Log(5)\\ \Rightarrow\ x=(-3\ Log(5))/(Log(5)+5\ Log(8))\\x\approx{-0.40213677...}`