Question

$27 to \: the \: power \: x - 1 = 9to \: the \: power \: x + 2$
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Answer 1

Answer:

7

Step-by-step explanation:

Lets write the equation according to the question.

27^x-1 = 9^x+2

We can reduce the numbers 27 and 9 to base 3.

3^ 3(x-1) = 3^2(x-2) [ 27 = 3^3 and 9 = 3^2 . The exponents are multiplied to the existing exponents.]

3^3x-3 = 3^2x + 2

Now , as the bases of the RHS and LHS have matched , we will remove the base.

3x-3 = 2x+4.

3x-2x = 4+3= 7 [Using transposition]

Hence , x = 7.

Hope it helps.