Write the exact answer using either base-10 and base- logarithms.

Question

17^7x=13^-x+10

Answer 1

ln 17^7x = ln 13^{(-x + 10)}

7x ln 17 = (-x + 10) ln 13

7x ln 17 = - x ln 13 + 10 ln 13

7 x ln 17 + x ln 13 = 10 ln 13

x(7 ln 17 + ln 13) = 10 ln 13

x = 10 ln 13 / (7 ln 17 + ln 13)