Example Question - logarithmic form conversion
Here are examples of questions we've helped users solve.
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 \(x = 11\).
Converting Exponential to Logarithmic Form
The image shows a handwritten question asking to convert the form of the following equation, specifically from exponential form to logarithmic form, and vice versa. The given equation is: 7^x = 2401 To convert from exponential form to logarithmic form, you apply the basic definition of logarithms. If a^b = c, then log_a(c) = b. Applying this to the given equation, you get: log_7(2401) = x. To find the value of x, you need to determine what power of 7 gives you 2401. 2401 is 7 raised to the fourth power since 7 * 7 * 7 * 7 = 2401. Therefore, the logarithmic form of the equation is: log_7(2401) = 4. Hence, x = 4.
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