What is the answer to 5^{16}+5^x=5^{x+7}+5^9 ?

The answer to 5^{16}+5^x=5^{x+7}+5^9 is x=9

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5^{16}+5^x=5^{x+7}+5^9

5^{16} + 5^{x} = 5^{x + 7} + 5^{9}

x = 9

Solution steps

5^{16} + 5^{x} = 5^{x + 7} + 5^{9}

Subtract

5^{x + 7}

from both sides

5^{16} + 5^{x} - 5^{x + 7} = 5^{x + 7} + 5^{9} - 5^{x + 7}

Simplify

5^{16} + 5^{x} - 5^{x + 7} = 1953125

Factor

5^{16} + 5^{x} - 5^{x + 7} : 5^{16} - 78124 \cdot 5^{x}

5^{16} - 78124 \cdot 5^{x} = 1953125

Move

5^{16}

to the right side

- 78124 \cdot 5^{x} = 1953125 - 5^{16}

Divide both sides by

- 78124

5^{x} = - \frac{1953125 - 5 ^{16}}{78124}

Apply exponent rules

x = 9

3^{5 x + 8} = 9^{2 x - 4}

5^{4 x - 3} = 33

5^{4 x - 3} = 30

2^{x} = 3600000

5^{5 x + 12} = 25

What is the answer to 5^{16}+5^x=5^{x+7}+5^9 ?
The answer to 5^{16}+5^x=5^{x+7}+5^9 is x=9
Solve for x: 5^{16}+5^x=5^{x+7}+5^9
The solution is x=9