Solving Exponential Equations
Muhtasari
When the unknown sits in the exponent, ordinary algebra cannot reach it. Logarithms are the tool that brings it down to ground level. Taking the logarithm of both sides of \(a^x=b\) lets you slide the power out in front, turning an exponential equation into a linear one you can solve at once.
In this lesson you will solve equations like \(2^x=10\) by taking logarithms, using either base 10 or the natural logarithm. The key formula is \(x=\dfrac{\log b}{\log a}\), and you will see how it follows directly from the power law.
Malengo
- Solve equations of the form a to the power x equals b.
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- To solve a^x = b, the first step is to: A. divide both sides by a B. take logarithms of both sides C. square both sides D. subtract b Answer: B
- Solving 2^x = 10 gives x equal to: A. log 2 / log 10 B. log 10 / log 2 C. log(10/2) D. 10/2 Answer: B
- To 2 decimal places, the solution of 2^x = 10 is: A. 2.32 B. 3.32 C. 5.00 D. 1.43 Answer: B
- Solve e^x = 7 (to 2 decimal places). A. 0.85 B. 1.95 C. 2.71 D. 7.00 Answer: B
- The step x log a = log b leads to x equal to: A. log b - log a B. log b / log a C. log(b - a) D. log a / log b Answer: B
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Sehemu ya kitabu
Exponential and Logarithmic Equations
Use like bases to solve exponential equations.
"College Algebra: Exponential and Logarithmic Equations" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/6-6-exponential-and-logarithmic-equations. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
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