Logarithm math help?

Question

Solve for x. 

 

11^-8x = 15^-x-7

Answer 1

Take a logarithm

-8xLg(11) = (-x-7)Lg(15)

Simplify

8xLg(11) = xLg(15) +7Lg(15)

x(8Lg(11) -Lg(15)) = 7Lg(15)

x = 7Lg(15)/(8Lg(11) -Lg(15))

 

 

Answer 2

Apply the properties of logarithms to find x.

 

-8x log11 = -(x + 7)log15

 

-8x log11 = -x log15 - 7 log15

 

x(-8 log11 + log15) = -7 log15

 

x = -7 log15 / (-8 log11 + log15)

 

You can simplify further if you wish.