Solving the Logarithmic Equation: log(x) × log(x²) = log(15)
Logarithmic equations are fundamental in algebra and pre-calculus, often appearing in problems that require manipulating logarithmic properties and solving for variables. Also, one such equation, log(x) × log(x²) = log(15), may seem complex at first glance but becomes manageable with the right approach. This article will guide you through solving this equation step by step, explaining the underlying principles and verifying the solutions But it adds up..
Step-by-Step Solution
Step 1: Simplify the Equation Using Logarithmic Properties
The equation is:
log(x) × log(x²) = log(15)
First, simplify log(x²) using the power rule of logarithms:
$ \log(a^b) = b \times \log(a) $
Applying this rule to log(x²):
$ \log(x^2) = 2 \times \log(x) $
Substitute this back into the original equation:
$ \log(x) \times (2 \times \log(x)) = \
