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Chapter 12: Problem 22

Evaluate each expression without using a calculator. $$\log _{7} 49$$

Short Answer

Expert verified
The value of \(\log_{7} 49\) is 2.

Step by step solution

01

Understand the log notation

In this problem, we're dealing with logarithms. We have \(\log_{7} 49\). This is read as 'log base 7 of 49'. This notation represents the exponent or power to which the base number (7) must be raised to obtain the number inside the log (49).
02

Transform the log equation into an equivalent exponential equation

Use the formula for converting a logarithmic equation into an exponential equation. The logarithmic equation \(\log_{b} n = x\) is equivalent to the exponential equation \(b^x = n\). Therefore, for \(\log_{7} 49\), the equivalent exponential form is \(7^x = 49\)
03

Solve the equation for x

To finish solving, a knowledge of the powers of 7 is needed. We know that \(7^2 = 49\), thus we take \(x=2\) . Therefore, x, which is the value of \(\log_{7} 49\), equals to 2.

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Most popular questions from this chapter

Describe the relationship between an equation in logarithmic form and an equivalent equation in exponential form.

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