What is the answer to 5^{x-1}+5^{x-2}=30 ?

The answer to 5^{x-1}+5^{x-2}=30 is x=3

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5^{x-1}+5^{x-2}=30

5^{x - 1} + 5^{x - 2} = 30

x = 3

Solution steps

5^{x - 1} + 5^{x - 2} = 30

Factor

5^{x - 1} + 5^{x - 2} : 6 \cdot 5^{x - 2}

6 \cdot 5^{x - 2} = 30

Divide both sides by

6

5^{x - 2} = 5

Apply exponent rules

x - 2 = 1

Solve

x - 2 = 1 : x = 3

x = 3

5^{x + 4} \cdot 25 = 125

130 (5^{x - 2}) = 1 + 2 5^{x}

(\frac{3}{5})^{x} = 7^{1 - x}

\frac{1 0 ^{2}}{1 0 ^{x}} = 10

2^{5 x} = 3^{x + 2}

What is the answer to 5^{x-1}+5^{x-2}=30 ?
The answer to 5^{x-1}+5^{x-2}=30 is x=3
Solve for x: 5^{x-1}+5^{x-2}=30
The solution is x=3