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Using Logarithms to Solve Exponential Equations and Inequalities (VCE SSCE Mathematical Methods): Flashcards

Using Logarithms to Solve Exponential Equations and Inequalities

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$\log_a b = x$

Exponentiation

$\frac{\log_b c}{\log_b a}$

$\log_b c$ (log of number of interest)

$\log_b a$ (log of original base)

Stays the same

Larger exponents give smaller values

Set $f(x) = 0$ , solve using logarithms

Convert to logarithmic form

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Using Logarithms to Solve Exponential Equations and Inequalities (VCE SSCE Mathematical Methods): Flashcards

Practise the cards

Logarithmic form of ax=ba^x = bax=b

Logarithms are inverse of what operation?

Change of base formula for log⁡ac\log_a cloga​c

Numerator in change of base formula

Denominator in change of base formula

Inequality direction when base >1> 1>1

Inequality direction when 0<0 < 0< base <1< 1<1

Why inequality reverses when 0<0 < 0< base <1< 1<1

Finding x-intercepts of exponential graphs

Most direct method for exponential equations

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

The Index Laws

Rational Indices

Graphs of Exponential Functions

Solving Exponential Equations and Inequalities

Using Logarithms to Solve Exponential Equations and Inequalities

Exponential Models and Applications

Logarithms

Graphing Logarithmic Functions

Determining Rules for Graphs of Exponential and Logarithmic Functions

Solution of Exponential Equations Using Logarithms

Inverses

Exponential Growth and Decay

Determining Rules for Graphs of Exponential and Logarithmic Functions

Solution of Exponential Equations Using Logarithms

Inverses

Exponential Growth and Decay

Explore VCE SSCE Mathematical Methods Model Answers by Topics

The Index Laws

Rational Indices

Graphs of Exponential Functions

Solving Exponential Equations and Inequalities

Using Logarithms to Solve Exponential Equations and Inequalities

Exponential Models and Applications

Logarithms

Graphing Logarithmic Functions

Determining Rules for Graphs of Exponential and Logarithmic Functions

Solution of Exponential Equations Using Logarithms

Inverses

Exponential Growth and Decay

Determining Rules for Graphs of Exponential and Logarithmic Functions

Solution of Exponential Equations Using Logarithms

Inverses

Exponential Growth and Decay

Explore VCE SSCE Mathematical Methods Quizzes by Topics

The Index Laws

Rational Indices

Graphs of Exponential Functions

Solving Exponential Equations and Inequalities

Using Logarithms to Solve Exponential Equations and Inequalities

Exponential Models and Applications

Logarithms

Graphing Logarithmic Functions

Determining Rules for Graphs of Exponential and Logarithmic Functions

Solution of Exponential Equations Using Logarithms

Inverses

Exponential Growth and Decay

Determining Rules for Graphs of Exponential and Logarithmic Functions

Solution of Exponential Equations Using Logarithms

Inverses

Exponential Growth and Decay

Explore VCE SSCE Mathematical Methods Exam Questions by Topics

The Index Laws

Rational Indices

Graphs of Exponential Functions

Solving Exponential Equations and Inequalities

Using Logarithms to Solve Exponential Equations and Inequalities

Exponential Models and Applications

Logarithms

Graphing Logarithmic Functions

Determining Rules for Graphs of Exponential and Logarithmic Functions

Solution of Exponential Equations Using Logarithms

Inverses

Exponential Growth and Decay

Determining Rules for Graphs of Exponential and Logarithmic Functions

Solution of Exponential Equations Using Logarithms

Inverses

Exponential Growth and Decay

Logarithmic form of $a^x = b$

Change of base formula for $\log_a c$

Inequality direction when base $> 1$

Inequality direction when $0 <$ base $< 1$

Why inequality reverses when $0 <$ base $< 1$