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what is the value of $x$ when $\log x + \log 2 = 2$ ?

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Find limits using power and root laws

Full solution

Q. what is the value of

x

when

\log x + \log 2 = 2

?

Combine logarithms: Combine the logarithms on the left side using the product rule for logarithms, which states that $\log a + \log b = \log(ab)$ . $\log x + \log 2 = \log(2x)$
Set equal to $2$ : Set the combined logarithm equal to the right side of the equation. $\log(2x) = 2$
Convert to exponential form: Convert the logarithmic equation to its exponential form. The base of the logarithm is $10$ by default when no base is specified, so the equation becomes $10^2 = 2x$ . $\newline$ $10^2 = 2x$
Calculate $10^2$ : Calculate the value of $10^2$ . $\newline$ $10^2 = 100$
Set result equal: Set the result equal to $2x$ . $\newline$ $100 = 2x$
Divide by $2$ : Divide both sides of the equation by $2$ to solve for $x$ . $x = \frac{100}{2}$
Calculate $x$ : Calculate the value of $x$ . $x = 50$

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