What is the answer to solvefor t,2a^{t/3}=5 ?

The answer to solvefor t,2a^{t/3}=5 is t=(3ln(5/2))/(ln(a))

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solvefor t,2a^{t/3}=5

solve for

t, 2 a^{\frac{t}{3}} = 5

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

Solution steps

2 a^{\frac{t}{3}} = 5

Divide both sides by

2

a^{\frac{t}{3}} = \frac{5}{2}

Apply exponent rules

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

Solve

\frac{t}{3} ln (a) = ln (\frac{5}{2}) : t = \frac{3 ln ( \frac{5}{2} )}{ln ( a )}

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

5^{x + 5} = 1

8 1^{x} = 2 7^{x + 2}

2^{2 x} = 32

1 0^{4 x} = 20

3 \cdot 2^{\frac{x}{5}} = 150

What is the answer to solvefor t,2a^{t/3}=5 ?
The answer to solvefor t,2a^{t/3}=5 is t=(3ln(5/2))/(ln(a))