Solve for x: 5^(3x) = 625

Understand the Problem

The question is asking to solve for x in the equation 5^(3x) = 625. To solve for x will require the use of logarithms or rewriting numbers so they have the same base.

Answer

$x = \frac{4}{3}$

Steps to Solve

Rewrite 625 as a power of 5 We need to find an exponent such that $5$ raised to that exponent equals $625$. $5^1 = 5$ $5^2 = 25$ $5^3 = 125$ $5^4 = 625$ So, we can rewrite the equation as: $5^{3x} = 5^4$
Set the exponents equal to each other Since the bases are the same, we can set the exponents equal to each other: $3x = 4$
Solve for $x$ Divide both sides of the equation by 3: $x = \frac{4}{3}$

$\frac{4}{3}$

More Information

The solution to the equation $5^{3x} = 625$ is $x = \frac{4}{3}$.

Tips

A common mistake is to try to take the logarithm of both sides immediately without simplifying the equation first. While this approach would also work if done correctly, it introduces more steps and more opportunities for error. Another common mistake involves incorrectly simplifying exponential expressions, such as not recognizing that $625 = 5^4$.

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