I am currently learning about converting to log. However, My teacher did not explain converting to log with multiple variables.
Ex: 12^3 = (x^4)(y^3)(z^6)
Can anyone explain how to make that a logarithmic equation?

Question

02-05-2022
Mathematics

contestada

I am currently learning about converting to log. However, My teacher did not explain converting to log with multiple variables.
Ex: 12^3 = (x^4)(y^3)(z^6)
Can anyone explain how to make that a logarithmic equation?

Respuesta :

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jdoe0001 jdoe0001 · Answer 1 · 2022-05-03T00:15:32+02:00

[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\\\ \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]12^3~~ = ~~x^4 y^3 z^6\implies \log_{12}(x^4 y^3 z^6)=3 \\\\\\ \log_{12}(x^4)~~ + ~~\log_{12}(y^3)~~ + ~~\log_{12}(z^6)~~ = ~~3 \\\\\\ 4\log_{12}(x)~~ + ~~3\log_{12}(y)~~ + ~~6\log_{12}(z)~~ = ~~3[/tex]

I am currently learning about converting to log. However, My teacher did not explain converting to log with multiple variables. Ex: 12^3 = (x^4)*(y^3)*(z^6) Can anyone explain how to make that a logarithmic equation?

Respuesta :

Otras preguntas

I am currently learning about converting to log. However, My teacher did not explain converting to log with multiple variables.
Ex: 12^3 = (x^4)(y^3)(z^6)
Can anyone explain how to make that a logarithmic equation?