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Solve for a positive value of
x.

log_(x)(128)=7
Answer:

Solve for a positive value of $x$ . $\newline$ $\log _{x}(128)=7$ $\newline$ Answer:

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Find derivatives of logarithmic functions

Full solution

Q. Solve for a positive value of

x

.

\newline

\log _{x}(128)=7

\newline

Answer:

Understand the logarithmic equation: Understand the logarithmic equation. $\newline$ The equation $\log_{x}(128) = 7$ means that $x$ raised to the power of $7$ equals $128$ . $\newline$ Mathematically, this can be written as $x^7 = 128$ .
Convert to exponential form: Convert the logarithmic equation to an exponential form. $\newline$ To find the value of $x$ , we rewrite the equation in its exponential form: $\newline$ $x^7 = 128$
Solve for x: Solve for x. $\newline$ To solve for x, we need to take the seventh root of both sides of the equation: $\newline$ $x = 128^{1/7}$
Calculate seventh root of $128$ : Calculate the seventh root of $128$ . $128$ is $2$ raised to the power of $7$ (since $2^7 = 128$ ), so taking the seventh root of $128$ is the same as taking the seventh root of $2^7$ , which is $2$ . Therefore, $x = 2$ .

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