OpenStudy (anonymous):

10^(x+5) = 4e^(8-x)

OpenStudy (asnaseer):

use logs

OpenStudy (anonymous):

im stuck after i rewrite it in terms of logs. i get (x+5)(log10) = (8-x)(log4e)

OpenStudy (asnaseer):

your term on the right hand side is not correct

OpenStudy (asnaseer):

also - are you using log to represent log to base 10 or to base e?

OpenStudy (anonymous):

thats's the part I"m unsure of since there's both 10^(x+5) and e^(8-x)

OpenStudy (anonymous):

that's*

OpenStudy (asnaseer):

I would use base e

OpenStudy (asnaseer):

so your first step would be:\[10^{x+5}=4e^{8-x}\]then:\[\ln(10^{x+5})=\ln(4e^{8-x})\]which leads to:\[(x+5)\ln(10)=\ln(4)+\ln(e^{8-x})=\ln(4)+(8-x)\ln(e)=\ln(4)+(8-x)\]

OpenStudy (asnaseer):

then just gather the terms involving x on to the left hand side and solve

hero (hero):

\[10^{x+5} = 4e^{8-x}\] \[10^x \dot\ 10^5 = 4e^8 \dot\ e^{-x}\] \[10^xe^x = \frac{4e^8}{10^5}\] \[(10e)^x = \frac{4e^8}{10^5}\] \[x \ln(10e) = \ln\left(\frac{4e^8}{10^5}\right)\] \[x = \frac{\ln(4e^8) - \ln(10^5)}{\ln(10e)}\]