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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21.
Indices
21.1
Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)}
21.2
Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
21.3
Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)}
21.4
Indices: Negative exponents
21.5
Indices: Zero exponent: a0=1 a^0 = 1
21.6
Indices: Rational exponents
21.7
Combining laws of indices
21.8
Scientific notation
21.9
Convert between radicals and rational exponents
21.10
Solving for indices
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