How Do You Solve Logarithmic Equations with Coefficients?

[darshanpatel]

Homework Statement

Solve:

log₆(2x-5)+1=log₆(7x+10)

Homework Equations

-None-

The Attempt at a Solution

I know we will need to exponentiate both side by 6 to get rid of the log, or either take another log.

I need help with getting rid of the +1 on the left side of the = sign because that is what is baffling me.

 

[Muphrid]

Hint: $6^{1+a} = 6 \times 6^a$, doesn't it?

 

[darshanpatel]

log₆(2x-5)+1=log₆(7x+10)

6^{log₆(2x-5)+1}=6^{log₆(7x+10)}

6(2x-5)=7x+10

12x-30=7x+10

5x=40

x=8

I checked it and it worked, thanks for the help man!

 

[Chestermiller]

Homework Statement

Solve:

log₆(2x-5)+1=log₆(7x+10)

Homework Equations

-None-

The Attempt at a Solution

I know we will need to exponentiate both side by 6 to get rid of the log, or either take another log.


I need help with getting rid of the +1 on the left side of the = sign because that is what is baffling me.

log₆6 = ?

Chet