Question

I'm stuck. Can anyone help please?

Answer 1

log₉(x - 7) + log₉(x - 7) = 1

2 log₉(x - 7) = 1

log₉(x - 7) = 1/2

Take the base-9 antilogarithm of both sides; in other words, make both sides powers of 9:

$9^{\log_9(x-7)} = 9^{1/2}$

$9^{1/2}$ can also be written as √9 = 3, and $b^{\log_b(a)}=a$, so the equation reduces to

x - 7 = 3

Solve for x :

x = 10