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Bayani Gaba-gaba

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.

Nazarin Darasi

Barka da kammala darasi akan Solving Exponential Equations. Yanzu da kuka bincika mahimman raayoyi da raayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.

Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.

Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.

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