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Chapter 3: Problem 17

Evaluate the indicated expression. Do not use a calculator for these exercises. $$ \log 10000 $$

Short Answer

Expert verified
The logarithm of 10000 with base 10 can be rewritten as an exponential equation: \(10^x = 10000\). We can express 10000 as a power of 10: \(10^4 = 10000\). Since the exponent x is 4, the final answer is: \(\log{10000} = 4\).

Step by step solution

01

Rewrite the Expression as an Exponential Equation

Recall that common logarithm has a base of 10. We want to find x in the equation: \( 10^x = 10000 \).
02

Express 10000 as a power of 10

Given that \(10^1 = 10\), \(10^2 = 100\), \(10^3 = 1000\), and so on, we rewrite 10000 as: \(10^4 = 10000\).
03

Determine the exponent x

Comparing with our previously rewritten expression, \( 10^x = 10000 \) and \(10^4 = 10000\), we can see that the exponent x is 4.
04

Write the final answer

The value of the logarithm is the exponent, which is \(x = 4\). Therefore: \[ \log{10000} = 4 \].

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