Solve for the exact value of x. log_(7)(6x)+4log_(7)(3)=3 Answer:

Apply power rule: Apply the power rule of logarithms to simplify the second term. The power rule states that log_b(a^c) = c * log_b(a). We can apply this rule to the second term 4log_7(3) to simplify it. 4log_7(3) = log_7(3^4)Rewrite using simplified term: Rewrite the equation using the simplified second term. log_7(6x) + log_7(3^4) = 3Combine logarithmic terms: Combine the logarithmic terms using the product rule. The product rule states that log_b(a) + log_b(c) = log_b(a * c). We can combine the two logarithmic terms on the left side of the equation. log_7(6x * 3^4) = 3Calculate to simplify: Calculate 3^4 to simplify the equation further. 3^4 = 3 * 3 * 3 * 3 = 81 log_7(6x * 81) = 3Rewrite in exponential form: Rewrite the equation in exponential form. The equation log_7(6x * 81) = 3 can be rewritten in exponential form as 7^3 = 6x * 81. 7^3 = 6x * 81Calculate value of x: Calculate 7^3 to find the value on the right side of the equation. 7^3 = 7 * 7 * 7 = 343 343 = 6x * 81Divide both sides of the equation by 81 to solve for x. 343 / 81 = 6x x = 343 / (6 * 81)Calculate the value of x. x = 343 / (6 * 81) x = 343 / 486 x = 7 / 9

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Solve for the exact value of
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log_(7)(6x)+4log_(7)(3)=3
Answer:

Solve for the exact value of $x$ . $\newline$ $\log _{7}(6 x)+4 \log _{7}(3)=3$ $\newline$ Answer:

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Calculus

Find derivatives of logarithmic functions

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Q. Solve for the exact value of

x

\newline

\log _{7}(6 x)+4 \log _{7}(3)=3

\newline

Answer:

Apply power rule: Apply the power rule of logarithms to simplify the second term. $\newline$ The power rule states that $\log_b(a^c) = c \cdot \log_b(a)$ . We can apply this rule to the second term $4\log_7(3)$ to simplify it. $\newline$ $4\log_7(3) = \log_7(3^4)$
Rewrite using simplified term: Rewrite the equation using the simplified second term. $\newline$ $\log_7(6x) + \log_7(3^4) = 3$
Combine logarithmic terms: Combine the logarithmic terms using the product rule. $\newline$ The product rule states that $\log_b(a) + \log_b(c) = \log_b(a \cdot c)$ . We can combine the two logarithmic terms on the left side of the equation. $\newline$ $\log_7(6x \cdot 3^4) = 3$
Calculate to simplify: Calculate $3^4$ to simplify the equation further. $\newline$ $3^4 = 3 \times 3 \times 3 \times 3 = 81$ $\newline$ $\log_7(6x \times 81) = 3$
Rewrite in exponential form: Rewrite the equation in exponential form. $\newline$ The equation $\log_7(6x \times 81) = 3$ can be rewritten in exponential form as $7^3 = 6x \times 81$ . $\newline$ $7^3 = 6x \times 81$
Calculate value of x: Calculate $7^3$ to find the value on the right side of the equation. $\newline$ $7^3 = 7 \times 7 \times 7 = 343$ $\newline$ $343 = 6x \times 81$
Calculate value of x: Calculate $7^3$ to find the value on the right side of the equation. $\newline$ $7^3 = 7 \times 7 \times 7 = 343$ $\newline$ $343 = 6x \times 81$ Divide both sides of the equation by $81$ to solve for x. $\newline$ $343 / 81 = 6x$ $\newline$ $x = 343 / (6 \times 81)$
Calculate value of x: Calculate $7^3$ to find the value on the right side of the equation. $\newline$ $7^3 = 7 \times 7 \times 7 = 343$ $\newline$ $343 = 6x \times 81$ Divide both sides of the equation by $81$ to solve for $x$ . $\newline$ $343 / 81 = 6x$ $\newline$ $x = 343 / (6 \times 81)$ Calculate the value of $x$ . $\newline$ $x = 343 / (6 \times 81)$ $\newline$ $x = 343 / 486$ $\newline$ $7^3 = 7 \times 7 \times 7 = 343$ $0$