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

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Using Logarithms to Solve Exponential Equations and Inequalities
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What is the logarithmic form of ax=ba^x = b?

log⁡ab=x\log_a b = x

Convert 2x=112^x = 11 to logarithmic form.

x=log⁡211x = \log_2 11

What is the change of base formula for log⁡ac\log_a c?

log⁡bclog⁡ba\frac{\log_b c}{\log_b a}

In change of base formula, what is the numerator?

Log of the number you're interested in

First step to solve 32x−1=283^{2x-1} = 28 is to:

Convert to logarithmic form

When base > 1 in inequality 2x≥52^x \geq 5, the direction:

Stays the same

When 0 < base < 1 in inequality, the direction:

Reverses

Why does log⁡100.7\log_{10} 0.7 cause inequality flip?

It is negative

To find x-intercept of f(x)=2×10x−4f(x) = 2 \times 10^x - 4, set:

f(x)=0f(x) = 0 and solve

Asymptote of f(x)=2×10x−4f(x) = 2 \times 10^x - 4 as x→−∞x \to -\infty:

y=−4y = -4

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

Show more

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

Show more

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 Flashcards 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

Show more

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

Show more

Determining Rules for Graphs of Exponential and Logarithmic Functions

Solution of Exponential Equations Using Logarithms

Inverses

Exponential Growth and Decay

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