What is the answer to (1.25^n)/(0.5^n)= 53/15 ?

The answer to (1.25^n)/(0.5^n)= 53/15 is n=(ln(53/15))/(ln(2.5))

Solve for n: (1.25^n)/(0.5^n)= 53/15

The solution is n=(ln(53/15))/(ln(2.5))

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\frac{1.2 5 ^{n}}{0. 5 ^{n}} = \frac{53}{15}

n = \frac{ln ( \frac{53}{15} )}{ln ( 2.5 )}

Decimal Notation

n = 1.37755 \dots

Solution steps

\frac{1.2 5 ^{n}}{0. 5 ^{n}} = \frac{53}{15}

Apply exponent rules

(n + lo g_{1.25} (\frac{1}{2}) (- n)) ln (1.25) = ln (\frac{53}{15})

Solve

(n + lo g_{1.25} (\frac{1}{2}) (- n)) ln (1.25) = ln (\frac{53}{15}) : n = \frac{ln ( \frac{53}{15} )}{ln ( 2.5 )}

n = \frac{ln ( \frac{53}{15} )}{ln ( 2.5 )}

Verify Solutions:

n = \frac{ln ( \frac{53}{15} )}{ln ( 2.5 )}

True

The solution is

n = \frac{ln ( \frac{53}{15} )}{ln ( 2.5 )}

(\frac{1}{4})^{x} + (\frac{1}{2})^{x} - 6 = 0

8 \cdot 3^{n - 1} - 21 = 51

3^{2 x} - 10 \times 3^{x} + 21 = 0

3^{2 x - 4} = 3^{5 x + 8}

y, x = 1 2^{1 - 0.1 y}

What is the answer to (1.25^n)/(0.5^n)= 53/15 ?
The answer to (1.25^n)/(0.5^n)= 53/15 is n=(ln(53/15))/(ln(2.5))
Solve for n: (1.25^n)/(0.5^n)= 53/15
The solution is n=(ln(53/15))/(ln(2.5))