Step-by-step explanation:
3^x - 14(3^-x) = 5
3^x - 14/3^x = 5
Multiplying through by 3^x;
3^x × 3^x - 3^x × 14/3^x = 3^x × 5
3^2x - 14 = 15^x
3^2x - 15^x - 14 = 0
3^x(3^x) - 5(3^ x) -14 = 0
let 3^x = y;
y(y) - 5(y) - 14 = 0
y^2 - 5y -14 = 0
Factoring;
(y - 7)(y + 2) = 0
y - 7 = 0 => y = 7
y + 2 = 0 => y = -2
y = 7 or -2
but y = 3^x
3^x = 7
Taking the logarithm of both sides;
log3^x = log7
xlog3 = log7
x = log7/log3
x = 1.771
3^x = -2
log3^x = log-2
xlog3 = log-2
x = log-2/log3
x = 0.631
x = 1.771 or 0.631.
