Respuesta :
x = 11.125
STEP - BY - STEP EXPLANATION
What to do?
Solve the given equation.
Given:
log (2x+ 9) = 1+ log(x- 8)
To solve, we will follow the steps below:
Step 1
Re-arrange by subtracting log(x-8) from both-side of the equation.
[tex]log(2x+9)-log(x-8)=1[/tex]Step 2
Apply the law of logarithm that is applicable to the given problem.
[tex]log\frac{(2x+9)}{(x-8)}=1[/tex]Step 3
Replace 1 by log10
Step 4
[tex]log\frac{(2x+9)}{(x-8)}=log10[/tex]Step 5
Cancel-out the log from both-side of the equation.
[tex]\frac{2x+9}{x-8}=10[/tex]Step 6
Cross - multiply
[tex]2x+9=10(x-8)[/tex]Step 7
Open the parenthesis.
[tex]2x+9=10x-80[/tex]Step 8
Collect like term.
[tex]10x-2x=80+9[/tex][tex]8x=89[/tex]Step 9
Divide both-side of the equation by 8
[tex]\frac{8x}{8}=\frac{89}{8}[/tex][tex]x=11.125[/tex]Therefore, the value of x is 11.125
