10*2^((3t)/(5))=1000 What is the solution of the equation? Round your answer, if necessary, to the nearest thousandth. t~~

Isolate exponential term: Simplify the equation by dividing both sides by 10 to isolate the exponential term. We have the equation 10*2^((3t)/(5))=1000. To simplify, we divide both sides by 10: 2^((3t)/(5)) = 1000 / 10 2^((3t)/(5)) = 100Convert to power of 2: Convert the right side of the equation to a power of 2. We know that 2^10 = 1024, which is close to 1000. However, since we need an exact value, we can use 2^6 = 64 and 2^7 = 128 to determine that 100 is not a power of 2. But we can express 100 as 2^2 * 5^2. Since we are looking for an expression with a base of 2, we can use the fact that 2^2 = 4 and 5^2 = 25, and 4 * 25 = 100. Therefore, we can write 100 as 2^2 * 5^2, but since we need a base of 2, we can only use 2^2 for this step: 2^((3t)/(5)) = 2^2Set exponents equal: Since the bases are equal, set the exponents equal to each other and solve for t. (3t)/(5) = 2 Now, we multiply both sides by 5 to solve for t: 3t = 2 * 5 3t = 10Solve for t: Divide both sides by 3 to solve for t. t = 10 / 3 t ≈ 3.333 (rounded to the nearest thousandth)

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10*2^((3t)/(5))=1000
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth.

t~~

$10 \cdot 2^{\frac{3 t}{5}}=1000$ $\newline$ What is the solution of the equation? $\newline$ Round your answer, if necessary, to the nearest thousandth. $\newline$ $t \approx$

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Algebra 2

Solve exponential equations using common logarithms

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10 \cdot 2^{\frac{3 t}{5}}=1000

\newline

What is the solution of the equation?

\newline

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

\newline

t \approx

Isolate exponential term: Simplify the equation by dividing both sides by $10$ to isolate the exponential term. $\newline$ We have the equation $10\cdot2^{(3t)/(5)}=1000$ . To simplify, we divide both sides by $10$ : $\newline$ $2^{(3t)/(5)} = \frac{1000}{10}$ $\newline$ $2^{(3t)/(5)} = 100$
Convert to power of $2$ : Convert the right side of the equation to a power of $2$ . $\newline$ We know that $2^{10} = 1024$ , which is close to $1000$ . However, since we need an exact value, we can use $2^6 = 64$ and $2^7 = 128$ to determine that $100$ is not a power of $2$ . But we can express $100$ as $2^2 \times 5^2$ . Since we are looking for an expression with a base of $2$ , we can use the fact that $2^2 = 4$ and $1000$ $0$ , and $1000$ $1$ . Therefore, we can write $100$ as $2^2 \times 5^2$ , but since we need a base of $2$ , we can only use $1000$ $5$ for this step: $\newline$ $1000$ $6$
Set exponents equal: Since the bases are equal, set the exponents equal to each other and solve for $t$ . $\newline$ $\frac{3t}{5} = 2$ $\newline$ Now, we multiply both sides by $5$ to solve for $t$ : $\newline$ $3t = 2 \times 5$ $\newline$ $3t = 10$
Solve for t: Divide both sides by $3$ to solve for t. $\newline$ $t = \frac{10}{3}$ $\newline$ $t \approx 3.333$ (rounded to the nearest thousandth)