Solve the Logarithmic Equation: n log_x a - Step by Step Guide

$n\log_xa=$

To solve this problem, we need to transform the expression $n\log_xa$ using the properties of logarithms.

• Step 1: Identify the expression: We are given $n\log_xa$, where $\log_xa$ is the logarithm of $a$ to the base $x$, and $n$ is a coefficient.
• Step 2: Use the power property of logarithms: The power property of logarithms states that if we have a logarithmic term multiplied by a coefficient $n$, like $n\log_b(a)$, it can be rewritten as $\log_b(a^n)$.
• Step 3: Apply the power property: By applying this property to $n\log_xa$, we rewrite it as $\log_x(a^n)$. This is because multiplying the logarithmic term by an external coefficient is equivalent to taking the argument $a$ to the power of that coefficient, $n$.
• Step 4: Conclusion about the transformation: This transformation demonstrates how the power property helps simplify expressions involving logarithms by turning multiplication into an exponentiation within the logarithm itself.

Therefore, the expression $n\log_xa$ can be transformed and expressed as $\log_xa^n$ by using the power property of logarithms.