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

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lfryerda | High School Teacher | (Level 2) Educator

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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` .

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