What is the answer to 50 1/3 =\sqrt[n]{50} ?

The answer to 50 1/3 =\sqrt[n]{50} is n=(ln(50))/(ln(151/3))

Solve for n: 50 1/3 =\sqrt[n]{50}

The solution is n=(ln(50))/(ln(151/3))

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n = \frac{ln ( 50 )}{ln ( \frac{151}{3} )}

Decimal Notation

n = 0.99830 \dots

Solution steps

Convert mixed numbers to improper fractions:

50 \frac{1}{3} = \frac{151}{3}

Multiply both sides by

3

Simplify

Switch sides

Divide both sides by

3

Apply exponent rules

\frac{1}{n} ln (50) = ln (\frac{151}{3})

Solve

\frac{1}{n} ln (50) = ln (\frac{151}{3}) : n = \frac{ln ( 50 )}{ln ( \frac{151}{3} )}

n = \frac{ln ( 50 )}{ln ( \frac{151}{3} )}

Verify Solutions:

n = \frac{ln ( 50 )}{ln ( \frac{151}{3} )}

True

The solution is

n = \frac{ln ( 50 )}{ln ( \frac{151}{3} )}

2^{y} = 4

5^{2 x} - 2 \cdot 5^{x} = 24

x + 3^{x} = 4

3 (2^{2 x}) - 13 (2^{x}) + 12 = 0

2^{x + 7} = 256

What is the answer to 50 1/3 =\sqrt[n]{50} ?
The answer to 50 1/3 =\sqrt[n]{50} is n=(ln(50))/(ln(151/3))
Solve for n: 50 1/3 =\sqrt[n]{50}
The solution is n=(ln(50))/(ln(151/3))