What is the answer to ln((t-64)/(125))=-0.07t ?

The answer to ln((t-64)/(125))=-0.07t is t=(\W_{0}((35)/(4e^{\frac{31.36)/7)})+4.48}{0.07}

Solve for t: ln((t-64)/(125))=-0.07t

The solution is t=(\W_{0}((35)/(4e^{\frac{31.36)/7)})+4.48}{0.07}

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ln (\frac{t - 64}{125}) = - 0.07 t

t = \frac{W _{0} ( \frac{35}{4 e ^{\frac{31.36}{7}}} ) + 4.48}{0.07}

Decimal Notation

t = 65.29399 \dots

Solution steps

ln (\frac{t - 64}{125}) = - 0.07 t

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (\frac{t - 64}{125})} = e^{- 0.07 t}

Simplify

e^{l n (\frac{t - 64}{125})} : \frac{t - 64}{125}

\frac{t - 64}{125} = e^{- 0.07 t}

Multiply both sides by

125

\frac{t - 64}{125} \cdot 125 = e^{- 0.07 t} \cdot 125

Simplify

t - 64 = e^{- 0.07 t} \cdot 125

Solve

t - 64 = e^{- 0.07 t} \cdot 125 : t = \frac{W _{0} ( \frac{35}{4 e ^{\frac{31.36}{7}}} ) + 4.48}{0.07}

t = \frac{W _{0} ( \frac{35}{4 e ^{\frac{31.36}{7}}} ) + 4.48}{0.07}

Verify Solutions:

t = \frac{W _{0} ( \frac{35}{4 e ^{\frac{31.36}{7}}} ) + 4.48}{0.07}

True

The solution is

t = \frac{W _{0} ( \frac{35}{4 e ^{\frac{31.36}{7}}} ) + 4.48}{0.07}

x (ln (x) - 1) = 0

- ln (x) = - 1

lo g_{3} (x) - lo g_{3} (x + 13) = - 3

5 ln (7 x - 9) + 4 = 34

lo g_{2} (x^{2} + 3 x) = 2

What is the answer to ln((t-64)/(125))=-0.07t ?
The answer to ln((t-64)/(125))=-0.07t is t=(\W_{0}((35)/(4e^{\frac{31.36)/7)})+4.48}{0.07}
Solve for t: ln((t-64)/(125))=-0.07t
The solution is t=(\W_{0}((35)/(4e^{\frac{31.36)/7)})+4.48}{0.07}