Solve for R

Question

log5(7r-7)=log5(r^2+5)

Answer 1

Aisha, if log₅ of both are equal, then they are equal.

 

7r - 7 = r² + 5

r² - 7r + 12 = 0

(r - 4)(r - 3) = 0

 

r - 4 = 0

r = 4

 

r - 3 = 0

r = 3

 

Hope this helps!

Answer 2

Exponentiate both sides, since they have a common base of 5 that seems to be most agreeable.

 

7r - 7 = r² + 5

0 = r² - 7r + 12

0 = (r - 4)(r - 3)

 

so, r = 3 and r = 4 are candidates for the solution.

Since neither leads to an illegal logarithm (one whose argument is a negative number), both solutions are valid.