# solve the following logarithmic equation exact answers only log(2x+8)=1+log(x-3)must show work

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To solve this equation we need to use the logarithm division rule.

`log(2x+8)=1+log(x-3)` move log to left side

`log(2x+8)-log(x-3)=1` combine with division rule

`log({2x+8}/{x-3})=1` write as exponential equation

`{2x+8}/{x-3}=10^1` clear fraction

`2x+8=10(x-3)` expand right side

`2x+8=10x-30` simplify

`38=8x` simplify again

`x=38/8`

`x=19/4`

**The solution is `x=19/4` .**

2x+8/x-3=10^1

2x+8=10(x-3)

2x+8=10x-30

38=8x

x=19/4