Solve for x, rounding to the nearest hundredth. 23*2^(x)=16 Answer:

Isolate exponential term: Isolate the exponential term by dividing both sides of the equation by 23. \[ \frac{23 \cdot 2^x}{23} = \frac{16}{23} \] \[ 2^x = \frac{16}{23} \]Take natural logarithm: Take the natural logarithm (ln) of both sides to solve for x. \[ \ln(2^x) = \ln\left(\frac{16}{23}\right) \] Using the property of logarithms that $\ln(a^b) = b \cdot \ln(a)$, we can rewrite the left side of the equation. \[ x \cdot \ln(2) = \ln\left(\frac{16}{23}\right) \]Divide by ln(2): Divide both sides by $\ln(2)$ to solve for x. \[ x = \frac{\ln\left(\frac{16}{23}\right)}{\ln(2)} \]Calculate x: Calculate the value of x using a calculator. \[ x \approx \frac{\ln\left(\frac{16}{23}\right)}{\ln(2)} \] \[ x \approx \frac{\ln(16) - \ln(23)}{\ln(2)} \] \[ x \approx \frac{2.77258872 - 3.13549422}{0.69314718} \] \[ x \approx \frac{-0.3629055}{0.69314718} \] \[ x \approx -0.52373663 \] Rounded to the nearest hundredth, $x \approx -0.52$.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for
x, rounding to the nearest hundredth.

23*2^(x)=16
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $23 \cdot 2^{x}=16$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Find trigonometric functions using a calculator

Full solution

Q. Solve for

x

, rounding to the nearest hundredth.

\newline

23 \cdot 2^{x}=16

\newline

Answer:

Isolate exponential term: Isolate the exponential term by dividing both sides of the equation by $23$ . $\newline$ $\frac{23 \cdot 2^x}{23} = \frac{16}{23}$ $\newline$ $2^x = \frac{16}{23}$
Take natural logarithm: Take the natural logarithm (ln) of both sides to solve for x. $\newline$ $\ln(2^x) = \ln\left(\frac{16}{23}\right)$ $\newline$ Using the property of logarithms that $\ln(a^b) = b \cdot \ln(a)$ , we can rewrite the left side of the equation. $\newline$ $x \cdot \ln(2) = \ln\left(\frac{16}{23}\right)$
Divide by ln( $2$ ): Divide both sides by $\ln(2)$ to solve for x. $\newline$ $x = \frac{\ln\left(\frac{16}{23}\right)}{\ln(2)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x \approx \frac{\ln\left(\frac{16}{23}\right)}{\ln(2)}$ $\newline$ $x \approx \frac{\ln(16) - \ln(23)}{\ln(2)}$ $\newline$ $x \approx \frac{2.77258872 - 3.13549422}{0.69314718}$ $\newline$ $x \approx \frac{-0.3629055}{0.69314718}$ $\newline$ $x \approx -0.52373663$ $\newline$ Rounded to the nearest hundredth, $x \approx -0.52$ .