10*3^((5t)/(4))=800 What is the solution of the equation? Round your answer, if necessary, to the nearest thousandth. t~~

Isolate exponential term: Isolate the exponential term. We start by dividing both sides of the equation by 10 to isolate the exponential term on one side. 10 * 3^((5t)/4) = 800 3^((5t)/4) = 800 / 10 3^((5t)/4) = 80Apply logarithm: Apply the logarithm to both sides. To solve for t, we take the natural logarithm (ln) of both sides of the equation. ln(3^((5t)/4)) = ln(80)Use power property of logarithms: Use the power property of logarithms. The power property of logarithms states that ln(a^b) = b * ln(a). We apply this property to simplify the left side of the equation. (5t)/4 * ln(3) = ln(80)Isolate t: Isolate t. To solve for t, we multiply both sides of the equation by 4/5 and divide by ln(3). t = (4 * ln(80)) / (5 * ln(3))Calculate value of t: Calculate the value of t. Now we use a calculator to find the numerical value of t. t = (4 * ln(80)) / (5 * ln(3)) t ≈ (4 * 4.38202663467) / (5 * 1.09861228867) t ≈ 17.52810653868 / 5.49306144335 t ≈ 3.19153829085Round answer: Round the answer to the nearest thousandth. t ≈ 3.192

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

10*3^((5t)/(4))=800
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth.

t~~

$10 \cdot 3^{\frac{5 t}{4}}=800$ $\newline$ What is the solution of the equation? $\newline$ Round your answer, if necessary, to the nearest thousandth. $\newline$ $t \approx$

View step-by-step help

Home

Math Problems

Algebra 2

Solve exponential equations using common logarithms

Full solution

10 \cdot 3^{\frac{5 t}{4}}=800

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

t \approx

Isolate exponential term: Isolate the exponential term. $\newline$ We start by dividing both sides of the equation by $10$ to isolate the exponential term on one side. $\newline$ $10 \cdot 3^{(5t)/4} = 800$ $\newline$ $3^{(5t)/4} = \frac{800}{10}$ $\newline$ $3^{(5t)/4} = 80$
Apply logarithm: Apply the logarithm to both sides. $\newline$ To solve for $t$ , we take the natural logarithm ( $\ln$ ) of both sides of the equation. $\newline$ $\ln(3^{(\frac{5t}{4})}) = \ln(80)$
Use power property of logarithms: Use the power property of logarithms. $\newline$ The power property of logarithms states that $\ln(a^b) = b \cdot \ln(a)$ . We apply this property to simplify the left side of the equation. $\newline$ $\frac{5t}{4} \cdot \ln(3) = \ln(80)$
Isolate t: Isolate $t$ . $\newline$ To solve for $t$ , we multiply both sides of the equation by $\frac{4}{5}$ and divide by $\ln(3)$ . $\newline$ $t = \frac{4 \cdot \ln(80)}{5 \cdot \ln(3)}$
Calculate value of t: Calculate the value of $t$ . $\newline$ Now we use a calculator to find the numerical value of $t$ . $\newline$ $t = \frac{4 \cdot \ln(80)}{5 \cdot \ln(3)}$ $\newline$ $t \approx \frac{4 \cdot 4.38202663467}{5 \cdot 1.09861228867}$ $\newline$ $t \approx \frac{17.52810653868}{5.49306144335}$ $\newline$ $t \approx 3.19153829085$
Round answer: Round the answer to the nearest thousandth. $t \approx 3.192$