Question - Solving Logarithmic Equations by Converting to Exponential Form
mathsolving logarithmic equationsconverting to exponential formlogarithm base 10exponential form conversion
Solution:
To solve the logarithmic equation $$\log(2x + 4) = 2$$, we can rewrite the equation in its exponential form. The base of the logarithm is 10 by default when no base is specified. With this in mind, the equation becomes:$$10^{\log(2x + 4)} = 10^2$$Since $$10^{\log(x)} = x$$, we have:$$2x + 4 = 10^2$$$$2x + 4 = 100$$Next, we solve for $$x$$ by isolating the variable:$$2x = 100 - 4$$$$2x = 96$$Divide both sides by 2 to find $$x$$:$$x = \frac{96}{2}$$$$x = 48$$Hence, the solution to the equation $$\log(2x + 4) = 2$$ is $$x = 48$$.
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