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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22.
Indices
22.1
Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)}
22.2
Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
22.3
Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)}
22.4
Indices: Negative exponents
22.5
Indices: Zero exponent: a0=1 a^0 = 1
22.6
Indices: Rational exponents
22.7
Combining laws of indices
22.8
Scientific notation
22.9
Convert between radicals and rational exponents
22.10
Solving for indices
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