What is the answer to 15*5^n=53*2^n ?

The answer to 15*5^n=53*2^n is n=(ln(53)-ln(15))/(ln(5)-ln(2))

Solve for n: 15*5^n=53*2^n

The solution is n=(ln(53)-ln(15))/(ln(5)-ln(2))

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15 \cdot 5^{n} = 53 \cdot 2^{n}

n = \frac{ln ( 53 ) - ln ( 15 )}{ln ( 5 ) - ln ( 2 )}

Decimal Notation

n = 1.37755 \dots

Solution steps

15 \cdot 5^{n} = 53 \cdot 2^{n}

Apply exponent rules

ln (15) + n ln (5) = ln (53) + n ln (2)

Solve

ln (15) + n ln (5) = ln (53) + n ln (2) : n = \frac{ln ( 53 ) - ln ( 15 )}{ln ( 5 ) - ln ( 2 )}

n = \frac{ln ( 53 ) - ln ( 15 )}{ln ( 5 ) - ln ( 2 )}

a^{x} = b

1 6^{3 x - 1} = 8^{x + 2}

e^{x} = - 4

e^{x} = 16

3^{2 x - 3} - 4 \cdot 3^{x - 2} + 1 = 0

What is the answer to 15*5^n=53*2^n ?
The answer to 15*5^n=53*2^n is n=(ln(53)-ln(15))/(ln(5)-ln(2))
Solve for n: 15*5^n=53*2^n
The solution is n=(ln(53)-ln(15))/(ln(5)-ln(2))