Logarithms

Question

Solve the equation if possible. Give the exact solution if there is one. 

log(x-6)+log(x-8)=log195

Answer 1

log(x-6) + log(x-8) = log(195)

 

Use the identity log(a)+log(b) = log(ab):

 

log( (x-6)(x-8) ) = log(195)

 

Hence:

 

(x-6)(x-8) = 195

x² - 14x + 48 = 195

x² - 14x - 147 = 0

 

Factors to:

 

(x-21)(x+7) = 0

x = 21 or -7