What is the answer to 130(5^{x-2})=1+25^x ?

The answer to 130(5^{x-2})=1+25^x is x=1,x=-1

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130(5^{x-2})=1+25^x

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

x = 1, x = - 1

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

5^{x} = u

130 u \cdot 5^{- 2} = 1 + (u)^{2}

Solve

130 u \cdot 5^{- 2} = 1 + u^{2} : u = 5, u = \frac{1}{5}

u = 5, u = \frac{1}{5}

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 5 : x = 1

Solve

5^{x} = \frac{1}{5} : x = - 1

x = 1, x = - 1

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

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

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

5^{4 x - 1} = 25

r, x^{r} = 0

What is the answer to 130(5^{x-2})=1+25^x ?
The answer to 130(5^{x-2})=1+25^x is x=1,x=-1
Solve for x: 130(5^{x-2})=1+25^x
The solution is x=1,x=-1