Solve the logarithmic equation Be sure to reject any value o

Solve the logarithmic equation. Be sure to reject any value of x that is not in the of the Select the correct choice below and, if necessary, fill in the answer box to complete your choice The solution set is.(Type an answer in simplified form.) There is no solution.

Solution

Given

log₈ x +log₈ (7x-1) = 1

Using

log_b(m) + log_b(n) = log_b(mn)     // if the base of log terms are same then we can multiply the terms inside log

log₈ (x(7x-1)) = 1

distributing \"x\" over the bracket

log₈ (7x² - x) = 1

7x² - x = 8¹                    //        log_b a = c   => a = b^c

7x² - x = 8

7x² - x - 8 = 0

7x² -8x +7x -8 = 0

x(7x - 8) +1(7x-8) = 0

(7x - 8)(x + 1) = 0

x = 8/7   or x = -1

for x = -1       we cannot consider this solution as log is not defined for negative numbers

therefore the solution is x = 8/7