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Chapter 16: Problem 3

If \(\log _{s}(x)=-1.8\), find \(x\). a) \(0.00483\) b) \(0.0169\) c) \(0.0552\) d) \(0.0783\)

Short Answer

Expert verified
a) 0.0021 b) 0.0169 c) 3.98 d) 63.09 Answer: b) 0.0169

Step by step solution

01

Transform into exponential form

To convert the equation \(\log _{s}(x)=-1.8\) into its exponential form, we can use the rule: \(\log _{b}(a)=c \Rightarrow b^c = a\). Here, \(b=s\), \(a=x\), and \(c=-1.8\). Hence, we have: $$ s^{-1.8} = x $$
02

Calculate \(x\) using the known value of \(s\)

Since we know that \(s=10\), we can substitute that value into the equation we obtained in step 1: $$ 10^{-1.8} = x $$
03

Simplify the equation

Calculate the value of \(10^{-1.8}\), which equals: $$ x = 0.0158489 $$
04

Check the answer with the given options

We have to find which option is closest to the calculated value of \(x\) in step 3. Comparing \(0.0158489\) with the given options, we can find that the closest option is: $$ x \approx 0.0169 $$ The answer is b) \(0.0169\).

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