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Worked solution

Translate a logarithmic equation into index form

Solve the equation log⁡2x=−1\log_2x=-1.

CJC · O Level revision · Example 9

Answer

x=12x=\dfrac12.

Compare your reasoning

Use the definition of logarithm

log⁡2x=−1 ⟹ x=2−1=12\log_2x=-1\ \Longrightarrow\ x=2^{-1}=\frac12

Base 2 is positive and not 1; the resulting argument 1/2 is positive, satisfying the logarithm domain.

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