11^9x =17^-x+5 Write the exact answer using either base-10 or base-e logarithms.

Question

11^9x =17^-x+5 Write the exact answer using either base-10 or base-e logarithms.

Answer 1

11^9x = 17^(5-x)

9xlog11 = (5-x)log17= 5log17 -xlog17

9xlog11+xlog17 = 5log17

x(9log11+log17) = 5log17

x = 5log17/(9log11+log17)

x = about 0.5802371423

= about 0.58

check the solution

11^9(.58) = 17^(-.58+5)

11^5.22= 17^4.42

272,942=274526

close enough given rounding approximations

this all assumes you meant 11^9x = 17^(-x+5) and did Not mean 11^9x = 17^-x +5

which leads to a different result, less than the above

Answer 2