Solve for x, rounding to the nearest hundredth. 10^(x)=68 Answer:

Write Equation to Solve: Write down the equation that needs to be solved. We have the equation 10^(x) = 68. We need to solve for x.Apply Logarithm: Apply the logarithm to both sides of the equation to solve for x. Taking the logarithm base 10 of both sides, we get log(10^(x)) = log(68).Simplify Using Logarithm Property: Simplify the equation using the property of logarithms that log(a^b) = b*log(a). This gives us x*log(10) = log(68). Since log(10) is 1, the equation simplifies to x = log(68).Calculate Log Value: Calculate the value of log(68) using a calculator. x = log(68) ≈ 1.83250891270624Round to Nearest Hundredth: Round the value of x to the nearest hundredth. x ≈ 1.83

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Solve for
x, rounding to the nearest hundredth.

10^(x)=68
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $10^{x}=68$ $\newline$ Answer:

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Precalculus

Solve exponential equations using logarithms

Full solution

Q. Solve for

x

, rounding to the nearest hundredth.

\newline

10^{x}=68

\newline

Answer:

Write Equation to Solve: Write down the equation that needs to be solved. $\newline$ We have the equation $10^{x} = 68$ . $\newline$ We need to solve for $x$ .
Apply Logarithm: Apply the logarithm to both sides of the equation to solve for $x$ . Taking the logarithm base $10$ of both sides, we get $\log(10^{x}) = \log(68)$ .
Simplify Using Logarithm Property: Simplify the equation using the property of logarithms that $\log(a^b) = b\log(a)$ . This gives us $x\log(10) = \log(68)$ . Since $\log(10)$ is $1$ , the equation simplifies to $x = \log(68)$ .
Calculate Log Value: Calculate the value of $\log(68)$ using a calculator. $x = \log(68) \approx 1.83250891270624$
Round to Nearest Hundredth: Round the value of $x$ to the nearest hundredth. $x \approx 1.83$