What is the answer to 2*3^{4t}=5^{-t} ?

The answer to 2*3^{4t}=5^{-t} is t=-(ln(2))/(ln(405))

Solve for t: 2*3^{4t}=5^{-t}

The solution is t=-(ln(2))/(ln(405))

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2 \cdot 3^{4 t} = 5^{- t}

t = - \frac{ln ( 2 )}{ln ( 405 )}

Decimal Notation

t = - 0.11544 \dots

Solution steps

2 \cdot 3^{4 t} = 5^{- t}

Apply exponent rules

ln (2) + 4 t ln (3) = - t ln (5)

Solve

ln (2) + 4 t ln (3) = - t ln (5) : t = - \frac{ln ( 2 )}{ln ( 405 )}

t = - \frac{ln ( 2 )}{ln ( 405 )}

4^{x + 2} = 64

2^{x} = 4^{x + 1}

4^{0.2 x} + 6 = 43

3^{- x} = 243

1 2^{x^{2} + 5 x - 4} = 1 2^{2 x + 6}

What is the answer to 2*3^{4t}=5^{-t} ?
The answer to 2*3^{4t}=5^{-t} is t=-(ln(2))/(ln(405))
Solve for t: 2*3^{4t}=5^{-t}
The solution is t=-(ln(2))/(ln(405))