6*2^((x)/(4))=222 What is the solution of the equation? Round your answer, if necessary, to the nearest thousandth. x~~

Isolate exponential term: Isolate the exponential term. To solve for x, we first need to isolate the term containing the variable x, which is 2^(x/4). We do this by dividing both sides of the equation by 6. 6 * 2^(x/4) = 222 2^(x/4) = 222 / 6 2^(x/4) = 37Take logarithm of sides: Take the logarithm of both sides. To solve for the exponent x/4, we take the logarithm of both sides of the equation. We can use the natural logarithm (ln) or the logarithm base 2 (log2) for convenience. Here, we'll use the natural logarithm. ln(2^(x/4)) = ln(37)Apply power rule: Apply the power rule of logarithms. The power rule of logarithms states that ln(a^b) = b * ln(a). We apply this rule to the left side of the equation. (x/4) * ln(2) = ln(37)Solve for x: Solve for x. Now we need to solve for x by multiplying both sides of the equation by 4 and then dividing by ln(2). x = (4 * ln(37)) / ln(2)Calculate x value: Calculate the value of x. Using a calculator, we find the value of x. x ≈ (4 * ln(37)) / ln(2) x ≈ (4 * 3.610918) / 0.693147 x ≈ 14.443672 / 0.693147 x ≈ 20.839

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

6*2^((x)/(4))=222
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth.

x~~

$6 \cdot 2^{\frac{x}{4}}=222$ $\newline$ What is the solution of the equation? $\newline$ Round your answer, if necessary, to the nearest thousandth. $\newline$ $x \approx$

View step-by-step help

Home

Math Problems

Algebra 2

Solve exponential equations using common logarithms

Full solution

6 \cdot 2^{\frac{x}{4}}=222

\newline

What is the solution of the equation?

\newline

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

\newline

x \approx

Isolate exponential term: Isolate the exponential term. $\newline$ To solve for $x$ , we first need to isolate the term containing the variable $x$ , which is $2^{x/4}$ . We do this by dividing both sides of the equation by $6$ . $\newline$ $6 \cdot 2^{x/4} = 222$ $\newline$ $2^{x/4} = \frac{222}{6}$ $\newline$ $2^{x/4} = 37$
Take logarithm of sides: Take the logarithm of both sides. $\newline$ To solve for the exponent $x/4$ , we take the logarithm of both sides of the equation. We can use the natural logarithm (ln) or the logarithm base $2$ (log $_2$ ) for convenience. Here, we'll use the natural logarithm. $\newline$ $\ln(2^{x/4}) = \ln(37)$
Apply power rule: Apply the power rule of logarithms. $\newline$ The power rule of logarithms states that $\ln(a^b) = b \cdot \ln(a)$ . We apply this rule to the left side of the equation. $\newline$ $\frac{x}{4} \cdot \ln(2) = \ln(37)$
Solve for x: Solve for x. $\newline$ Now we need to solve for x by multiplying both sides of the equation by $4$ and then dividing by $\ln(2)$ . $\newline$ $x = \frac{4 \cdot \ln(37)}{\ln(2)}$
Calculate x value: Calculate the value of x. $\newline$ Using a calculator, we find the value of $x$ . $\newline$ $x \approx (4 \times \ln(37)) / \ln(2)$ $\newline$ $x \approx (4 \times 3.610918) / 0.693147$ $\newline$ $x \approx 14.443672 / 0.693147$ $\newline$ $x \approx 20.839$