Question

What is the solution to log Subscript 5 Baseline (10 x minus 1) = log Subscript 5 Baseline (9 x + 7)
x = six-nineteenths
x = eight-nineteenths
x = 7
x = 8

Answer 1

Since log_5 is one-to-one, set the arguments equal:
10x − 1 = 9x + 7
x = 8

Check domain: 10(8)−1 = 79 > 0 and 9(8)+7 = 79 > 0, so x = 8 is valid.