How do you solve 8^(x-2) = 32^(x+10)?

1 Answer
Josh Tran
Apr 27, 2018

x = -28

Explanation:

The first step to solving this equation is changing the bases so that they are equal. To do this, find a number that can be raised to an exponent to equal each base. In this case, 2 can be raised to the third power to equal 8 and raised to the fifth power to equal 32:

2^3 = 8 | 2^5 = 32

Leaving us with:

(2^3)^(x-2) = (2^5)^(x+10)

Using a special property of exponents, we can multiply the exponents on each side of the equation:

3(x - 2) = 3x - 6 | 5(x + 10) = 5x + 50

Leaving us with:

2^(3x-6) = 2^(5x+50)

Now that the bases are equal, we know that the exponents are also equal:

3x - 6 = 5x + 50

Now all we need to do is solve for x using algebra:

2x = -56
x = -28**

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