Exponential Functions & Logarithms (Grade 12 NSC Matric Mathematics): Quizzes

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Exponential Functions & Logarithms
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What is the general form of an exponential function?

f(x)=bxf(x) = b^x where b>0b > 0 and b≠1b ≠ 1

What happens to an exponential function when b>1b > 1?

Function increases (exponential growth)

Why must x>0x > 0 when taking logarithms?

Because (positive number)anyvalue^{any value} > 0

What is 25=322^5 = 32 in logarithmic form?

5=log2325 = log_2 32

What is the value of loga1log_a 1 for any valid base aa?

00

Using the power law, what does log3(274)log_3(27^4) equal?

1212

What is the change of base formula for logaxlog_a x?

rac{log_b x}{log_b a}

What is the domain of f(x)=logbxf(x) = log_b x?

x:x>0,x∈R{x : x > 0, x ∈ ℝ}

What is the vertical asymptote of y=logbxy = log_b x?

x=0x = 0

How are exponential and logarithmic graphs related?

Reflections about line y=xy = x

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