-15*2^(-0.5 x)=-90 What is the solution of the equation? Round your answer, if necessary, to the nearest thousandth. x~~

Write equation: Write down the given equation. We have the equation -15*2^(-0.5 x)=-90.Divide by -15: Divide both sides of the equation by -15 to isolate the exponential term. -90 / -15 = 2^(-0.5 x) / -15 6 = 2^(-0.5 x)Apply logarithm: Apply the logarithm to both sides of the equation to solve for x. log(6) = log(2^(-0.5 x)) Use the power property of logarithms to bring down the exponent. log(6) = -0.5 x * log(2)Isolate x: Isolate x by dividing both sides by -0.5 log(2). x = log(6) / (-0.5 * log(2))Calculate x: Calculate the value of x using a calculator. x = log(6) / (-0.5 * log(2)) x ≈ 5.169925001 / (-0.5 * 0.3010299957) x ≈ 5.169925001 / (-0.15051499785) x ≈ -34.343

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

-15*2^(-0.5 x)=-90
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth.

x~~

$-15 \cdot 2^{-0.5 x}=-90$ $\newline$ 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

Precalculus

Solve exponential equations using logarithms

Full solution

-15 \cdot 2^{-0.5 x}=-90

\newline

What is the solution of the equation?

\newline

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

\newline

x \approx

Write equation: Write down the given equation. $\newline$ We have the equation $-15 \cdot 2^{(-0.5 x)} = -90$ .
Divide by ext{-} $15$ : Divide both sides of the equation by ext{-} $15$ to isolate the exponential term. $\newline$ ext{-} $90$ / ext{-} $15$ = $2$ ^{( ext{-} $0$ . $5$ x)} / ext{-} $15$ $\newline$ $6 = 2^{( ext{-}0.5 x)}$
Apply logarithm: Apply the logarithm to both sides of the equation to solve for x. $\newline$ $\log(6) = \log(2^{-0.5 x})$ $\newline$ Use the power property of logarithms to bring down the exponent. $\newline$ $\log(6) = -0.5 x \cdot \log(2)$
Isolate x: Isolate x by dividing both sides by $-0.5 \log(2)$ . $\newline$ $x = \frac{\log(6)}{(-0.5 \cdot \log(2))}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x = \frac{\log(6)}{-0.5 \times \log(2)}$ $\newline$ $x \approx \frac{5.169925001}{-0.5 \times 0.3010299957}$ $\newline$ $x \approx \frac{5.169925001}{-0.15051499785}$ $\newline$ $x \approx -34.343$