Question

Algebra 2. Help please!
Explain why log₀3 and log₁3 do not exist.

Answer 1

`\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_0(3)=x\implies 0^x=3~\hfill \stackrel{\textit{so there's no \underline{x} value that will satisfy that}}{0^(anything)=0\qquad \qquad 0^0=unde fined} \\\\\\ \log_1(3)=x\implies 1^x=3\hfill \stackrel{\textit{so there's no \underline{x} value that will satisfy that either}}{1^(anything)=1}`

Answer 2

See below.

Explanation:

By the definition of a logarithm:-

If y = log0 3 then 3 = 0^y = 0 which is obviously wrong.

If y = log1 3 then 3 = 1 ^y = 1 which again is wrong.

Neither 0 nor 1 can be a base of logarithms. 0 to any power will equal 0 and 1 to any power equals 1.