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5*7^(2y)=175
Which of the following is the solution of the equation?
Choose 1 answer:
(A)
y=log_(7)(35)
(B)
y=(log_(35)(7))/(2)
(C)
y=(log_(7)(35))/(2)
(D)
y=log_(35)(7)

$5 \cdot 7^{2 y}=175$ $\newline$ Which of the following is the solution of the equation? $\newline$ Choose $1$ answer: $\newline$ (A) $y=\log _{7}(35)$ $\newline$ (B) $y=\frac{\log _{35}(7)}{2}$ $\newline$ (C) $y=\frac{\log _{7}(35)}{2}$ $\newline$ (D) $y=\log _{35}(7)$

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Product property of logarithms

Full solution

Q.

5 \cdot 7^{2 y}=175

\newline

Which of the following is the solution of the equation?

\newline

Choose

1

answer:

\newline

(A)

y=\log _{7}(35)

\newline

(B)

y=\frac{\log _{35}(7)}{2}

\newline

(C)

y=\frac{\log _{7}(35)}{2}

\newline

(D)

y=\log _{35}(7)

Divide by $5$ : Divide both sides of the equation by $5$ to isolate the term with the variable $y$ . $\newline$ Calculation: $5\cdot7^{2y} = 175 \Rightarrow 7^{2y} = \frac{175}{5} \Rightarrow 7^{2y} = 35$
Apply logarithm: Apply the logarithm with base $7$ to both sides of the equation to solve for $y$ . $\newline$ Calculation: $\log_7(7^{2y}) = \log_7(35)$
Simplify left side: Use the property of logarithms that $\log_b(b^x) = x$ to simplify the left side of the equation. $\newline$ Calculation: $2y = \log_7(35)$
Divide by $2$ : Divide both sides of the equation by $2$ to solve for $y$ . $\newline$ Calculation: $y = \frac{\log_7(35)}{2}$

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