Determine which $x$-value below is a solution of the equation $\log _ { 7 } \left( \frac { 5 } { 3 } x \right) = 3$.
$$x = \frac { 21 } { 125 } , x = \frac { 1029 } { 5 } , x = \frac { 189 } { 5 } , x = 21 , x = 15$$

A) $x = \frac { 21 } { 125 }$

B) $x = \frac { 1029 } { 5 }$

C) $x = \frac { 189 } { 5 }$

D) $x = 21$

E) $x = 15$

Question

Determine which $x$-value below is a solution of the equation $\log _ { 7 } \left( \frac { 5 } { 3 } x \right) = 3$.
$$x = \frac { 21 } { 125 } , x = \frac { 1029 } { 5 } , x = \frac { 189 } { 5 } , x = 21 , x = 15$$

A) $x = \frac { 21 } { 125 }$

B) $x = \frac { 1029 } { 5 }$

C) $x = \frac { 189 } { 5 }$

D) $x = 21$

E) $x = 15$

Quizplus · Accepted Answer

To solve the equation $\log_7\left(\frac{5}{3}x\right) = 3$, we first rewrite it in exponential form: $7^3 = \frac{5}{3}x$. Solving for $x$, we get $x = \frac{7^3 \cdot 3}{5} = \frac{343 \cdot 3}{5} = \frac{1029}{5}$.

Determine Which xxx -Value Below Is a Solution of the Equation log⁡7(53x)=3\log _ { 7 } \left( \frac { 5 } { 3 } x \right) = 3log7​(35​x)=3

Determine Which $x$ -Value Below Is a Solution of the Equation $\log _ { 7 } \left( \frac { 5 } { 3 } x \right) = 3$