Solving Exponential Equations
Akopọ
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.
Awọn Afojusun
- Solve equations of the form a to the power x equals b.
Akọ̀wé Ẹ̀kọ́
O wa lori ohun elo Green Bridge
Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.
Ìdánwò Ẹ̀kọ́
Oriire fun ipari ẹkọ lori Solving Exponential Equations. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.
- 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
O wa lori ohun elo Green Bridge
Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.
O wa lori ohun elo Green Bridge
Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.
Awọn Iwe Itọsọna Ti a Gba Nimọran
Ṣe Adaṣe Awọn Ibeere Idanwo Adaṣe
Ṣe o fẹ ṣe adaṣe awọn ibeere idanwo adaṣe nipa Solving Exponential Equations? Ṣe igbasilẹ ohun elo Green Bridge CBT lati wọle si awọn ibeere idanwo adaṣe ati awọn ayẹwo adaṣe kikun fun koko-ọrọ yii.
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