Question

Solve the following equation. 3^x−7=27^2x

use the exponent technique, you should use x-7=2x to cancel them out

Answer 1

I assume the equation is 3^(x−7) = 27^(2x). (If you meant 3^x − 7 = 27^(2x), say so.)

Solve 3^(x−7) = 27^(2x).
Write 27 = 3^3, so
27^(2x) = (3^3)^(2x) = 3^(6x).

Thus 3^(x−7) = 3^(6x) so the exponents are equal:
x − 7 = 6x
−7 = 5x
x = −7/5 = −1.4.

Check: x−7 = −42/5 and 6x = −42/5, so both sides equal 3^(−42/5).

Note: x−7 = 2x is incorrect here because 27 = 3^3, not 3^1.