/*! 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 969 Determine the value of \(\mathrm... [FREE SOLUTION] | 91影视

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Chapter 33: Problem 969

Determine the value of \(\mathrm{x}\) such that \(10^{\mathrm{x}}=3.142\).

Short Answer

Expert verified
The value of x for the equation \(10^x = 3.142\) is approximately \(x \approx 0.4971\).

Step by step solution

01

Write the equation in logarithmic form

To solve for x, we'll rewrite the equation \(10^{\mathrm{x}}=3.142\) in logarithmic form. To do this, we need to recall the basic relationship between exponential functions and logarithms: For any base, b, if \(b^y = x\), then we can write \(\log_{b}{x}=y\) In this case, the base is 10, and we have \(10^x = 3.142\). Hence, we rewrite the given equation as: \[\log_{10}{3.142} = x\]
02

Evaluate the logarithm

Now, we need to evaluate the common logarithm, \(\log_{10}{3.142}\). This can be done using a calculator or a logarithm table. In the case of a calculator, enter "log(3.142)" and press the equal sign. The result will be: \[x \approx 0.4971\]
03

Write the final answer

We have found that the value of x is approximately 0.4971. So, the solution for the given equation is: \[x \approx 0.4971\]

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