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Concept of logarithm. Basic logarithmic identity

Logarithm as the answer to the inverse problem for axa^x
For a>0a>0, a≠1a\neq1, b>0b>0, the number log⁡ab\log_a b is the unique exponent cc such that ac=ba^c=b. Basic logarithmic identities: alog⁡ab=ba^{\log_a b}=b and log⁡a(ax)=x\log_a(a^x)=x for x∈Rx\in\mathbb{R}. In Grade 11 you use them freely when simplifying exponentials and in substitutions for equations.
b>0b>0 is required — otherwise log⁡ab\log_a b is not defined in R\mathbb{R}
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