Solve for x, rounding to the nearest hundredth. 10^(2x)=10 Answer:

Set up equation: Set up the equation based on the given problem. We have the equation 10^(2x) = 10. To solve for x, we need to find the value of x that makes the equation true.Use logarithm property: Use the property of logarithms to solve for x. Since 10 is the base of the exponential function, we can take the logarithm with base 10 of both sides of the equation to isolate x. This gives us: log(10^(2x)) = log(10)Apply power rule: Apply the power rule of logarithms. The power rule states that log_b(a^c) = c * log_b(a), where b is the base, a is the argument, and c is the exponent. Applying this rule, we get: 2x * log(10) = log(10)Simplify equation: Simplify the equation. Since log(10) is equal to 1 (because 10 is the base of the common logarithm), the equation simplifies to: 2x * 1 = 1 Which further simplifies to: 2x = 1Solve for x: Solve for x. To find x, we divide both sides of the equation by 2: x = 1 / 2Convert to decimal: Convert the exact answer to a decimal rounded to the nearest hundredth. x = 1 / 2 = 0.50

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Solve for
x, rounding to the nearest hundredth.

10^(2x)=10
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $10^{2 x}=10$ $\newline$ Answer:

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Q. Solve for

x

, rounding to the nearest hundredth.

\newline

10^{2 x}=10

\newline

Answer:

Set up equation: Set up the equation based on the given problem. $\newline$ We have the equation $10^{2x} = 10$ . To solve for $x$ , we need to find the value of $x$ that makes the equation true.
Use logarithm property: Use the property of logarithms to solve for $x$ . Since $10$ is the base of the exponential function, we can take the logarithm with base $10$ of both sides of the equation to isolate $x$ . This gives us: $\log(10^{2x}) = \log(10)$
Apply power rule: Apply the power rule of logarithms. $\newline$ The power rule states that $\log_b(a^c) = c \cdot \log_b(a)$ , where $b$ is the base, $a$ is the argument, and $c$ is the exponent. Applying this rule, we get: $\newline$ $2x \cdot \log(10) = \log(10)$
Simplify equation: Simplify the equation. $\newline$ Since $\log(10)$ is equal to $1$ (because $10$ is the base of the common logarithm), the equation simplifies to: $\newline$ $2x \times 1 = 1$ $\newline$ Which further simplifies to: $\newline$ $2x = 1$
Solve for x: Solve for x. $\newline$ To find x, we divide both sides of the equation by $2$ : $\newline$ $x = \frac{1}{2}$
Convert to decimal: Convert the exact answer to a decimal rounded to the nearest hundredth. $x = \frac{1}{2} = 0.50$