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Chapter 12: Problem 15

Write each equation in its equivalent logarithmic form. $$13^{2}=x$$

Short Answer

Expert verified
The logarithmic form of the given exponential equation is \(log_{13}x = 2\).

Step by step solution

01

Identify the Base, Exponent and Result

Firstly, identify the base, exponent, and result in the given exponential equation. In the equation \(13^2 = x\), 13 is the base, 2 is the exponent, and x is the result.
02

Convert the Exponential form to Logarithmic form

Now we convert the equation from its exponential form to logarithmic form using the conversion rule mentioned before. This leads us to \(log_{13}x = 2\). This is now the logarithmic form of given equation.

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Most popular questions from this chapter

I can solve \(4^{x}=15\) by writing the equation in logarithmic form.

Solve each equation. $$5^{x^{2}-12}=25^{2 x}$$

Solve the system: $$\left\\{\begin{aligned}2 x &=11-5 y \\\3 x-2 y &=-12\end{aligned}\right.$$ (Section 4.3, Example 4)

Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution set. Verify this value by direct substitution into the equation. $$2^{x+1}=8$$

Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution set. Verify this value by direct substitution into the equation. $$\log _{3}(3 x-2)=2$$
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