Solve the exponential equation. Give answers correct to 3 decimal places. $5 ^ { 7 x } = 3125$
A)625
B)0.714
C)1.000
D)0.453
E)313

Question

Quizplus · Accepted Answer

To solve the exponential equation $5^{7x} = 3125$, we recognize that 3125 is a power of 5, specifically $5^5$. Therefore, we can set the exponents equal to each other since the bases are the same: $7x = 5$. Solving for $x$ gives $x = \frac{5}{7}$, which is approximately 0.714 when rounded to three decimal places.

Solve the Exponential Equation 57x=31255 ^ { 7 x } = 312557x=3125

Solve the Exponential Equation $5 ^ { 7 x } = 3125$