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4 votes
Solve 81^x = 27^^^x + 2.

A. x = 1
B. x = 2
C. x = 5
D. x = 6

User Josoroma
by
8.1k points

2 Answers

4 votes

Answer:

Explanation:

81^x=27^(x+2)

3^4=81 and 3^3=27

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

exponents are the same so we just take those

4x=3x+6

x=6

User Jaredsk
by
8.4k points
2 votes

For this case we must solve the following equation:


81 ^ x = 27^(x + 2)

We rewrite:


81 = 3 ^ 4\\27 = 3 ^ 3

Then, replacing:


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

For the bases to be equal then it must be fulfilled that:


4x = 3 (x + 2)\\4x = 3x + 6\\4x-3x = 6\\x = 6

Answer:


x = 6

Option D

User Mahdi Jedari
by
8.1k points

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