Solution of Exponential Equations Using Logarithms (VCE SSCE Mathematical Methods): Quizzes

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Solution of Exponential Equations Using Logarithms
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What is the equivalent logarithmic form of 2x=112^x = 11?

x=log211x = \log_2 11

Why can't we solve 2x=112^x = 11 using basic algebra?

The variable is in the exponent

What does 0.3x=50.3^x = 5 convert to in logarithmic form?

x=log0.35x = \log_{0.3} 5

To solve 32x1=283^{2x-1} = 28, what should you do first?

Convert to logarithmic form

For base a>1a > 1, what happens to inequality direction when converting axba^x \geq b?

Direction stays the same

For base 0<a<10 < a < 1, what happens when converting axba^x \geq b to logarithmic form?

Direction reverses

For logab\log_a b to exist, which conditions must be met?

a>0a > 0, a1a \neq 1, b>0b > 0

Are exponential functions with base between 0 and 1 increasing or decreasing?

Decreasing

What is the equivalent form of 2x52^x \geq 5?

xlog25x \geq \log_2 5

What is the equivalent form of 0.3x50.3^x \geq 5?

xlog0.35x \leq \log_{0.3} 5

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