What is the answer to 8^x+8^x=2^{100} ?

The answer to 8^x+8^x=2^{100} is x=33

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8^x+8^x=2^{100}

8^{x} + 8^{x} = 2^{100}

x = 33

Solution steps

8^{x} + 8^{x} = 2^{100}

Add similar elements:

8^{x} + 8^{x} = 2 \cdot 8^{x}

2 \cdot 8^{x} = 2^{100}

Divide both sides by

2

8^{x} = \frac{2 ^{100}}{2}

Simplify

8^{x} = 2^{99}

Apply exponent rules

3 x = 99

Solve

3 x = 99 : x = 33

x = 33

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5^{x} = 2^{2 x + 1}

2 9^{9 x - 4} = 125