What is the answer to 45(1.038)^t=48(1.025)^t ?

The answer to 45(1.038)^t=48(1.025)^t is t=(ln(16/15))/(ln(1.038)-ln(1.025))

Solve for t: 45(1.038)^t=48(1.025)^t

The solution is t=(ln(16/15))/(ln(1.038)-ln(1.025))

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45 (1.038)^{t} = 48 (1.025)^{t}

t = \frac{ln ( \frac{16}{15} )}{ln ( 1.038 ) - ln ( 1.025 )}

Decimal Notation

t = 5.12081 \dots

Solution steps

45 (1.038)^{t} = 48 (1.025)^{t}

Apply exponent rules

ln (45) + t ln (1.038) = ln (48) + t ln (1.025)

Solve

ln (45) + t ln (1.038) = ln (48) + t ln (1.025) : t = \frac{ln ( \frac{16}{15} )}{ln ( 1.038 ) - ln ( 1.025 )}

t = \frac{ln ( \frac{16}{15} )}{ln ( 1.038 ) - ln ( 1.025 )}

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1 = e^{\frac{- 1}{3} (1^{3} + 3 + 3 c)}

2^{x^{2} - 14} = \frac{1}{1024}

3^{2 x - 1} x^{9} = 3^{x + 2} x^{27}

What is the answer to 45(1.038)^t=48(1.025)^t ?
The answer to 45(1.038)^t=48(1.025)^t is t=(ln(16/15))/(ln(1.038)-ln(1.025))
Solve for t: 45(1.038)^t=48(1.025)^t
The solution is t=(ln(16/15))/(ln(1.038)-ln(1.025))