Solving Logarithmic Equations by Converting to Exponential Form
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 \(x = 11\).
