What is the answer to 125^x+5^{3x+1}=200 ?

The answer to 125^x+5^{3x+1}=200 is x=(ln(100/3))/(3ln(5))

Solve for x: 125^x+5^{3x+1}=200

The solution is x=(ln(100/3))/(3ln(5))

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12 5^{x} + 5^{3 x + 1} = 200

x = \frac{ln ( \frac{100}{3} )}{3 ln ( 5 )}

Decimal Notation

x = 0.72624 \dots

Solution steps

12 5^{x} + 5^{3 x + 1} = 200

Apply exponent rules

3 x ln (5) = ln (\frac{100}{3})

Solve

3 x ln (5) = ln (\frac{100}{3}) : x = \frac{ln ( \frac{100}{3} )}{3 ln ( 5 )}

x = \frac{ln ( \frac{100}{3} )}{3 ln ( 5 )}

(\frac{8191}{8192})^{x} = 0.5

10 0^{x + 1} = 2 5^{x + 1}

7^{3 x} = 3^{2 - x}

x, 3^{2 x} + 2 \cdot 3^{x + 1} = 16

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

What is the answer to 125^x+5^{3x+1}=200 ?
The answer to 125^x+5^{3x+1}=200 is x=(ln(100/3))/(3ln(5))
Solve for x: 125^x+5^{3x+1}=200
The solution is x=(ln(100/3))/(3ln(5))