Solving Logarithmic Equations | MathHelp.com

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Here we’re asked to solve for x in the equation: log base x of 144 = 2. Notice that we have a logarithmic equation, so let’s first convert the equation to exponential form. Remember that the base of the log represents the base of the power, the right side of the equation represents the exponent, and the number inside the log represents the result, so we have x…squared…= 144. Now, to solve for x, since x is squared, we simply take the square root of both sides of the equation to get x = plus or minus 12. Remember to always use plus or minus when taking the square root of both sides of an equation. However, notice that x represents the base of the logarithm in the original problem, and the base of a logarithm cannot be negative. Therefore, x cannot be equal to negative 12. So our final answer is x = 12.