Question

Log (2x+ 9) = 1+ log(x- 8)

Answer 1

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.

`log(2x+9)-log(x-8)=1`

Step 2

Apply the law of logarithm that is applicable to the given problem.

`log((2x+9))/((x-8))=1`

Step 3

Replace 1 by log10

Step 4

`log((2x+9))/((x-8))=log10`

Step 5

Cancel-out the log from both-side of the equation.

`(2x+9)/(x-8)=10`

Step 6

Cross - multiply

`2x+9=10(x-8)`

Step 7

Open the parenthesis.

`2x+9=10x-80`

Step 8

Collect like term.

`10x-2x=80+9`
`8x=89`

Step 9

Divide both-side of the equation by 8

`(8x)/(8)=(89)/(8)`
`x=11.125`

Therefore, the value of x is 11.125