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Chapter 8: Problem 4

Write the following using indices: (a) \(\log _{5} 625=4\) (b) \(\log _{2} 256=8\) (c) \(\log 0.0251=-1.6\) (d) \(\ln 17=2.8332\)

Short Answer

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Question: Rewrite the following logarithmic expressions in index notation. (a) \(\log _{5} 625=4\) (b) \(\log _{2} 256=8\) (c) \(\log 0.0251=-1.6\) (d) \(\ln 17=2.8332\) Answer: (a) \(5^4 = 625\) (b) \(2^8 = 256\) (c) \(10^{-1.6} = 0.0251\) (d) \(e^{2.8332} = 17\)

Step by step solution

01

(a) Rewrite \(\log _{5} 625=4\) in index notation

Using the logarithmic property, let's rewrite the equation as: \(5^4 = 625\)
02

(b) Rewrite \(\log _{2} 256=8\) in index notation

Using the logarithmic property, let's rewrite the equation as: \(2^8 = 256\)
03

(c) Rewrite \(\log 0.0251=-1.6\) in index notation

Since this is a common logarithm, we have \(\log x = \log_{10}x\). Therefore, let's rewrite the equation using the logarithmic property: \(10^{-1.6} = 0.0251\)
04

(d) Rewrite \(\ln 17=2.8332\) in index notation

Since this is a natural logarithm, it is understood as an expression with base \(e\). So we have \(\ln x = \log_{e}x\). Let's rewrite the equation as: \(e^{2.8332} = 17\)

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