Solved on Nov 21, 2023

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

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

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

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 $t$ .
$t=\frac{-2.703}{-0.223}$

STEP 9

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

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

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

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

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 $t$ .
$t=\frac{-2.703}{-0.223}$

STEP 9

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

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Find the value of ttt in the equation t=ln⁡(1,00014,954)ln⁡0.8t=\frac{\ln \left(\frac{1,000}{14,954}\right)}{\ln 0.8}t=ln0.8ln(14,9541,000​)​.

STEP 1

Assumptions1. The equation is given as t=ln⁡(1,00014,954)ln⁡0.8t=\frac{\ln \left(\frac{1,000}{14,954}\right)}{\ln0.8}t=ln0.8ln(14,9541,000​)​. . We need to find the value of ttt.3. The base of the logarithm is eee (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}14,9541,000​

STEP 3

Calculate the value of the fraction.1,00014,954≈0.0669\frac{1,000}{14,954} \approx0.066914,9541,000​≈0.0669

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

Calculate the value of the natural logarithm.ln⁡(0.)≈−0.223\ln(0.) \approx -0.223ln(0.)≈−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 ttt.t=−2.703−0.223t=\frac{-2.703}{-0.223}t=−0.223−2.703​

STEP 9

Calculate the value of ttt.t=−2.703−.223≈12.13t=\frac{-2.703}{-.223} \approx12.13t=−.223−2.703​≈12.13So, the value of ttt in the equation t=ln⁡(,00014,954)ln⁡.8t=\frac{\ln \left(\frac{,000}{14,954}\right)}{\ln.8}t=ln.8ln(14,954,000​)​ is approximately12.13.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

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

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

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

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

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

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

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

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

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

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