/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 Suppose \(\log a=203.4\) and \(\... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 12

Suppose \(\log a=203.4\) and \(\log b=205.4\). Evaluate \(\frac{b}{a}\).

Short Answer

Expert verified
\(\frac{b}{a} = 100\)

Step by step solution

01

Express \(\frac{b}{a}\) in terms of logarithms

To express the fraction in terms of logarithms, we'll take the logarithm of \(\frac{b}{a}\). Using the logarithm rule for division, we can rewrite this as \(\log b - \log a\).
02

Substitute the given values

Now, we substitute the given values of \(\log a = 203.4\) and \(\log b = 205.4\). So, we have \(\log b - \log a = 205.4 - 203.4\).
03

Simplify and evaluate

Now, simply evaluate the expression: \(205.4 - 203.4 = 2\)
04

Find \(\frac{b}{a}\) from the logarithm result

We have found that \(\log b - \log a = 2\). To find \(\frac{b}{a}\), we can use the inverse logarithm property, which is: If \(\log x = y\), then \(x = 10^y\). So, in our case, we have: \(\log \frac{b}{a} = 2\) \(\frac{b}{a} = 10^2\)
05

Calculate the value

Now, we simply need to calculate \(10^2\): \(\frac{b}{a} = 10^2 = 100\) So the value of \(\frac{b}{a}\) is 100.

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