Solved on Nov 21, 2023

Find the value of tt in the equation t=ln(1,00014,954)ln0.8t=\frac{\ln \left(\frac{1,000}{14,954}\right)}{\ln 0.8}.

STEP 1

Assumptions1. The equation is given as t=ln(1,00014,954)ln0.8t=\frac{\ln \left(\frac{1,000}{14,954}\right)}{\ln0.8}. . We need to find the value of tt.
3. The base of the logarithm is ee (natural logarithm).

STEP 2

First, we calculate the value of the fraction inside the logarithm in the numerator.
1,00014,954\frac{1,000}{14,954}

STEP 3

Calculate the value of the fraction.
1,00014,9540.0669\frac{1,000}{14,954} \approx0.0669

STEP 4

Next, we calculate the natural logarithm of this fraction.
ln(0.0669)\ln(0.0669)

STEP 5

Calculate the value of the natural logarithm.
ln(0.0669)2.703\ln(0.0669) \approx -2.703

STEP 6

Now, we calculate the natural logarithm of0.8 in the denominator.
ln(0.8)\ln(0.8)

STEP 7

Calculate the value of the natural logarithm.
ln(0.)0.223\ln(0.) \approx -0.223

STEP 8

Now that we have the values of the numerator and the denominator, we can substitute these into the equation to find the value of tt.
t=2.7030.223t=\frac{-2.703}{-0.223}

STEP 9

Calculate the value of tt.
t=2.703.22312.13t=\frac{-2.703}{-.223} \approx12.13So, the value of tt in the equation t=ln(,00014,954)ln.8t=\frac{\ln \left(\frac{,000}{14,954}\right)}{\ln.8} is approximately12.13.

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