Solving for exponents

Solving for exponents

By now, you should be very familiar with all the exponent rules. Not sure? Test yourself and try out the questions in this lesson. In this session, we will learn how to solving questions which have exponents as the unknowns.
Basic Concepts: Proportions, Model and solve one-step linear equations: ax=bax = b, xa=b\frac{x}{a} = b, Solving two-step linear equations using addition and subtraction: ax+b=cax + b = c, Combining the exponent rules
Related Concepts: Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)}, Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}, Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)}, Exponents: Negative exponents

Lessons

  • Introduction
    What are exponent rules?
  • 1.
    Find the number x
    a)
    (12)x=8 ( \frac{1}{2}{)^x} = 8

    b)
    4x3=112 \frac{4^x}{3} = \frac{1}{12}

    c)
    5x+4=125 {5^{x+4}} = \frac{1}{25}

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4.
Laws of Indices
4.1
Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)}
4.2
Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
4.3
Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)}
4.4
Indices: Negative indices
4.5
Zero index: a0=1 a^0 = 1
4.6
Rational indices
4.7
Combining laws of indices
4.8
Solving for indices
4.9
Standard form
AS-Level Maths
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