Consider the equation 4*10^(-3x)=18. Solve the equation for x. Express the solution as a logarithm in base-10 x= ◻ Approximate the value of x. Round your answer to the nearest thousandth. x~~◻

Isolate exponential term: Step 1: Isolate the exponential term. 4*10^(-3x) = 18 Divide both sides by 4 to isolate the exponential term. 10^(-3x) = 18 / 4 10^(-3x) = 4.5Apply logarithm: Step 2: Apply the logarithm to both sides. Take the base-10 logarithm of both sides to remove the exponent. log_10(10^(-3x)) = log_10(4.5) -3x = log_10(4.5)Solve for x: Step 3: Solve for x. Divide both sides by -3 to solve for x. x = log_10(4.5) / -3Approximate x value: Step 4: Approximate the value of x. Using a calculator, find log_10(4.5). log_10(4.5) ≈ 0.653 x ≈ 0.653 / -3 x ≈ -0.218

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Consider the equation
4*10^(-3x)=18.
Solve the equation for
x. Express the solution as a logarithm in base-10

x=

◻
Approximate the value of
x. Round your answer to the nearest thousandth.

x~~◻

Consider the equation $4\times 10^{-3x}=18$ . $\newline$ Solve the equation for $x$ . Express the solution as a logarithm in base $-10$ $\newline$ $x=$ $\square$ $\newline$ Approximate the value of $x$ . Round your answer to the nearest thousandth. $\newline$ $x\approx$ $\square$

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Precalculus

Properties of logarithms: mixed review

Full solution

Q. Consider the equation

4\times 10^{-3x}=18

\newline

Solve the equation for

x

. Express the solution as a logarithm in base

-10

\newline

x=

\square

\newline

Approximate the value of

x

. Round your answer to the nearest thousandth.

\newline

x\approx

\square

Isolate exponential term: Step $1$ : Isolate the exponential term. $\newline$ $4\times10^{(-3x)} = 18$ $\newline$ Divide both sides by $4$ to isolate the exponential term. $\newline$ $10^{(-3x)} = \frac{18}{4}$ $\newline$ $10^{(-3x)} = 4.5$
Apply logarithm: Step $2$ : Apply the logarithm to both sides. $\newline$ Take the base $-10$ logarithm of both sides to remove the exponent. $\newline$ $\log_{10}(10^{-3x}) = \log_{10}(4.5)$ $\newline$ $-3x = \log_{10}(4.5)$
Solve for x: Step $3$ : Solve for x. $\newline$ Divide both sides by $-3$ to solve for x. $\newline$ $x = \frac{\log_{10}(4.5)}{-3}$
Approximate x value: Step $4$ : Approximate the value of $x$ . Using a calculator, find $\log_{10}(4.5)$ . $\log_{10}(4.5) \approx 0.653$ $x \approx 0.653 / -3$ $x \approx -0.218$