3^x-14(3^-x)=5
Please show work

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.

vertical=18cm horizontal=18cm hypotenuse=25.5

step-by-step explanation: