What is the answer to 3^{2t+1}=5^{3t-1} ?

The answer to 3^{2t+1}=5^{3t-1} is t=(ln(15))/(3ln(5)-2ln(3))

Solve for t: 3^{2t+1}=5^{3t-1}

The solution is t=(ln(15))/(3ln(5)-2ln(3))

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3^{2 t + 1} = 5^{3 t - 1}

t = \frac{ln ( 15 )}{3 ln ( 5 ) - 2 ln ( 3 )}

Decimal Notation

t = 1.02925 \dots

Solution steps

3^{2 t + 1} = 5^{3 t - 1}

Apply exponent rules

(2 t + 1) ln (3) = (3 t - 1) ln (5)

Solve

(2 t + 1) ln (3) = (3 t - 1) ln (5) : t = \frac{ln ( 15 )}{3 ln ( 5 ) - 2 ln ( 3 )}

t = \frac{ln ( 15 )}{3 ln ( 5 ) - 2 ln ( 3 )}

1 4^{x} = 3

12.5 = 15 (1 - e^{- k (30)})

2800 = 4000 - 3000 e^{5 k}

3^{x + 4} = 6^{2 x - 5}

5 (2^{x}) = 4

What is the answer to 3^{2t+1}=5^{3t-1} ?
The answer to 3^{2t+1}=5^{3t-1} is t=(ln(15))/(3ln(5)-2ln(3))
Solve for t: 3^{2t+1}=5^{3t-1}
The solution is t=(ln(15))/(3ln(5)-2ln(3))