Question

What is the value of x in the equation?

Answer 1

\[(81)^{x+2}=27^{5x+4}\]

Answer 2

If you can write an equation of one power equaling another power, and the bases are equal then the exponents are equal.
For example, if
\(a^x = a^y\)
Then x = y
Ok so far?

Answer 3

Yes

Answer 4

Notice in this case that both 81 and 27 are powers of 3.
Rewrite the equation as two powers of 3 that are equal to each other.
Then the exponents are equal.
Then solve for x.

Answer 5

Got it

(3^4)^x+2=(3^3)^5x+4

4x+8=15x+12

x=-4/11

Answer 6

\((3^4)^{x+2}=(3^3)^{5x+4}\)

Answer 7

Correct.