Question

How do you solve 8e^4x+8=15 using natural log with e? Thank you!

Answer 1

`8e^(4x+8)= 15\\ e^(4x+8)=(15)/(8)\\ 4x+8=\ln (15)/(8)\\ 4x=\ln (15)/(8)-8\\ x=(1)/(4)\ln (15)/(8)-2`

Answer 2

The question brought up in the comments is deciding between whether your problem is
`8e^4x+8=15` ((8e^4)x) or
`8e^(4x)+8=15` ((8e^(4x)). There's also the third interpretation,
`8e^(4x+8)=15` (using parentheses, 8e^(4x+8)).

I'll assume it's the second of these:


`8e^(4x)+8=15`

`8e^(4x)=7`

`e^(4x)=\frac78`

`\ln(e^(4x))=\ln\frac78`

`4x\ln e=\ln\frac78`

`4x=\ln\frac78`

`x=\frac14\ln\frac78`

- - -

If instead it's the third possibility,


`8e^(4x+8)=15`

`e^(4x+8)=\frac{15}8`

`\ln e^(4x+8)=\ln\frac{15}8`

`(4x+8)\ln e=\ln\frac{15}8`

`4x+8=\ln\frac{15}8`

`4x=\ln\frac{15}8-8`

`x=\frac14\ln\frac{15}7-2`