What is the answer to 25*90^n=60*6^n ?

The answer to 25*90^n=60*6^n is n=(ln(12/5))/(ln(15))

Solve for n: 25*90^n=60*6^n

The solution is n=(ln(12/5))/(ln(15))

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25 \cdot 9 0^{n} = 60 \cdot 6^{n}

n = \frac{ln ( \frac{12}{5} )}{ln ( 15 )}

Decimal Notation

n = 0.32328 \dots

Solution steps

25 \cdot 9 0^{n} = 60 \cdot 6^{n}

Apply exponent rules

ln (25) + n ln (90) = ln (60) + n ln (6)

Solve

ln (25) + n ln (90) = ln (60) + n ln (6) : n = \frac{ln ( \frac{12}{5} )}{ln ( 15 )}

n = \frac{ln ( \frac{12}{5} )}{ln ( 15 )}

3^{2 x} - 3^{x} - 30 = 0

3^{3 x} - 3^{2 x + 1} - 3^{x} + 3 = 0

7^{x} = 6^{x + 7}

7^{2 + x} = \frac{1}{4 9 ^{x + 3}}

3^{x} = 53

What is the answer to 25*90^n=60*6^n ?
The answer to 25*90^n=60*6^n is n=(ln(12/5))/(ln(15))
Solve for n: 25*90^n=60*6^n
The solution is n=(ln(12/5))/(ln(15))