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42 votes
42 votes
1/27^-x=81^2x+2 find x​

User Max Murphy
by
2.4k points

1 Answer

22 votes
22 votes

Answer:

Explanation:

81

=

3

4

and

27

=

3

3

, so this equation can also be written as

3

4

x

=

3

3

(

x

+

2

)

=

3

3

x

+

6

.

Since the bases are now the same, we can equate exponents to get

4

x

=

3

x

+

6

so that

x

=

6

(technically this equating of exponents requires the fact that exponential functions (with base not equal to 1) are one-to-one functions).

(do u understand?)

User Helpa
by
2.9k points