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Solve the following logarithm problem for the positive solution for
x.

log_(x)343=(3)/(2)
Answer:

Solve the following logarithm problem for the positive solution for $x$ . $\newline$ $\log _{x} 343=\frac{3}{2}$ $\newline$ Answer:

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Quotient property of logarithms

Full solution

Q. Solve the following logarithm problem for the positive solution for

x

.

\newline

\log _{x} 343=\frac{3}{2}

\newline

Answer:

Understand the logarithmic equation: Understand the logarithmic equation. $\newline$ The given logarithmic equation is $\log_{x}343=\frac{3}{2}$ , which means that $x$ raised to the power of $\frac{3}{2}$ equals $343$ .
Convert to exponential form: Convert the logarithmic equation to exponential form. $\newline$ Using the definition of a logarithm, we can rewrite the equation as $x^{\frac{3}{2}} = 343$ .
Find base of exponent: Find the base of the exponent that results in $343$ . We know that $7^3 = 343$ , so we can rewrite $343$ as $7^3$ .
Set bases equal: Set the expression with the base $x$ equal to the expression with base $7$ . Now we have $x^{3/2} = 7^3$ . Since the exponents are equal, we can set the bases equal to each other.
Solve for x: Solve for x. $\newline$ To find $x$ , we need to find a number that when raised to the power of $(3)/(2)$ gives $7^3$ . We can take the cube root of both sides and then square it to isolate $x$ . $\newline$ $(x^{(3/2)})^{(2/3)} = (7^3)^{(2/3)}$ $\newline$ $x = 7^2$ $\newline$ $x = 49$

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