What is the answer to solvefor t,40=120^{0.4t}+25 ?

The answer to solvefor t,40=120^{0.4t}+25 is t=(ln(15))/(0.4ln(120))

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solvefor t,40=120^{0.4t}+25

solve for

t, 40 = 12 0^{0.4 t} + 25

t = \frac{ln ( 15 )}{0.4 ln ( 120 )}

Decimal Notation

t = 1.41412 \dots

Solution steps

40 = 12 0^{0.4 t} + 25

Switch sides

12 0^{0.4 t} + 25 = 40

Move

25

to the right side

12 0^{0.4 t} = 15

Apply exponent rules

0.4 t ln (120) = ln (15)

Solve

0.4 t ln (120) = ln (15) : t = \frac{ln ( 15 )}{0.4 ln ( 120 )}

t = \frac{ln ( 15 )}{0.4 ln ( 120 )}

(\frac{1}{5})^{x - 2} = 2 5^{x - 2}

5^{x + 1} + 5^{x} + 5^{x - 2} - 151 = 0

2^{2 x} - 2^{x} - 12 = 0

4 + 3^{5 x} = 8

(\frac{1}{8})^{x + 3} = 1 6^{x - 4}

What is the answer to solvefor t,40=120^{0.4t}+25 ?
The answer to solvefor t,40=120^{0.4t}+25 is t=(ln(15))/(0.4ln(120))