Question - Solving Logarithmic Equations by Converting to Exponential Form
mathsolving logarithmic equationslogarithmic form conversionconverting to exponential formlogarithm rule
Solution:
To solve the given logarithmic equation $$\log_4(5x + 9) = 3$$, you can begin by converting the logarithmic form to exponential form. The basic logarithm rule states that if $$\log_b(A) = C$$, then $$b^C = A$$.Applying this rule here gives:$$4^3 = 5x + 9$$Now, calculate the left side:$$4^3 = 4 \times 4 \times 4 = 64$$So the equation becomes:$$64 = 5x + 9$$Now, subtract 9 from both sides to isolate the term containing $$x$$:$$64 - 9 = 5x$$$$55 = 5x$$Finally, divide both sides by 5 to solve for $$x$$:$$x = 55 / 5$$$$x = 11$$Therefore, the solution to the equation is $$x = 11$$.
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