How do you solve for x in Log x + Log (3x-13)=1?

1 Answer
Jul 20, 2018

x=5 only

Explanation:

If the question just says log, we can safely assume that it means log_10

log_10x+log_10(3x-13)=1

log_10 x(3x-13)=1
Recall: log_a b+log_a c=log_a bc

x(3x-13)=10^1
Recall: If log_a b=c then a^c=b

x(3x-13)=10

3x^2-13x-10=0

(3x+2)(x-5)=0

x=-2/3 or x=5

But x=-2/3 is not a solution since you cannot log negative numbers so x=5 is the solution only