Solve for x

1. log (x+9) = log (2x-7)

2. log (x-1) ^2=log (-5x-1)

Lets first solve the first one:

log (x+9) = log (2x-7)

Convert the logarithmic equation to an exponential equation.

10^ log (x+9) = 10^ log (2x-7)

Remember that 10^ logx = x, so

x+9=2x-7

Move values with 'x' to the right hand side.

7+9=2x-x

Combine like terms.

16=x so,

x=16

Check:

log (x+9) = log (2x-7)

If x=16

log (16+9) = log (2 (16) - 7)

log25 = log (32-7)

log25 = log25

x=16 is a solution.

Solve the second one like i solved this one, try it