Question

Given that q=7^x express the equation 7^{2x − 1} + 6 × 7^{x − 1} =1 interval of q.Hence or otherwise,find the value of x in the equation 7^{2x − 1} + 6 × 7^{x − 1} =1.

Answer 1

7^2x·7⁻¹ + 6×7^x·7⁻¹=1
^q2/₇ + ⁶/₇q =1
q² + 6q=7
q² + 6q −7=0
q² +7q−q−7=0
q(q+7) −1(q+7)=0
(q+7)(q−1) =0
    q=−7
q=1