The Use of Logarithms with GPs (HSC SSCE Mathematics Advanced): Flashcards

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The Use of Logarithms with GPs
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What equation type to find GP terms?

Exponential equations with nn in the exponent

Two methods for exponential equations

Trial-and-error and logarithms

What are exponential inequations?

Equations with nn in the index position

Behavior when base > 1

Powers increase as index increases

Behavior when base < 1

Powers decrease as index increases

Change-of-base formula

logbx=log10xlog10b\log_b x = \frac{\log_{10} x}{\log_{10} b}

Memory aid for change-of-base

Log of the number over log of the base

Logarithmic law for powers

log10an=nlog10a\log_{10} a^n = n \log_{10} a

First step solving exponential inequation

Write down the corresponding equation

Rounding rule for 'which year' questions

Round up to the next whole number

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