Name: Exponential equations: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 53 s
Description: If 9^x+2 = 27^x, what is the value of x? Try it, then watch the animated solution.

The bases

9

and

27

are different, but both are powers of

3

:

9 = 3^2

and

27 = 3^3

.

Replace each base. A power of a power multiplies the exponents:

3^{2(x+2)} = 3^{3x}

.

Both sides are now powers of

3

. They are equal only if the exponents are equal:

2(x + 2) = 3x

.

Distribute:

2x + 4 = 3x

. Subtract

2x

from both sides:

4 = x

.

Check with

x = 4

:

9^6

is six pairs of

3

s and

27^4

is four triples of

3

s. Both are

3^{12}

.

Traps:

2

forgets to distribute,

\tfrac{4}{5}

adds

2x

instead of subtracting, and

{-6}

swaps the exponents.

Try it first