What is the answer to 500*5^{y/3}=1 ?

The answer to 500*5^{y/3}=1 is y=-(3ln(500))/(ln(5))

Solve for y: 500*5^{y/3}=1

The solution is y=-(3ln(500))/(ln(5))

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500 \cdot 5^{\frac{y}{3}} = 1

y = - \frac{3 ln ( 500 )}{ln ( 5 )}

Decimal Notation

y = - 11.58405 \dots

Solution steps

500 \cdot 5^{\frac{y}{3}} = 1

Divide both sides by

500

5^{\frac{y}{3}} = \frac{1}{500}

Apply exponent rules

\frac{y}{3} ln (5) = ln (\frac{1}{500})

Solve

\frac{y}{3} ln (5) = ln (\frac{1}{500}) : y = - \frac{3 ln ( 500 )}{ln ( 5 )}

y = - \frac{3 ln ( 500 )}{ln ( 5 )}

6^{x} = 1296

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

1 0^{x} = 0.01

- 100 \cdot 2^{0.5 y} = - 5

7^{x^{2} - 3 x + 2} = 1

What is the answer to 500*5^{y/3}=1 ?
The answer to 500*5^{y/3}=1 is y=-(3ln(500))/(ln(5))
Solve for y: 500*5^{y/3}=1
The solution is y=-(3ln(500))/(ln(5))