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Nana76 [90]
3 years ago
7

If 3 to the power y = x then y = ?

Mathematics
1 answer:
Oksanka [162]3 years ago
6 0

Answer:

y=\log_3(x)


Step-by-step explanation:

3^y=x

\ln(3^y)=\ln(x)

y\ln(3)=\ln(x)

y=\frac{\displaystyle\ln(x)}{\displaystyle\ln(3)}

but if

f(x)=\frac{\displaystyle\ln(x)}{\displaystyle\ln(3)}

then since

f(3)=\frac{\displaystyle\ln(3)}{\displaystyle\ln(3)}=1

f(x)=\log_3(x)

so

y=\log_3(x)


or


3^y=x

\log_3(3^y)=\log_3(x)

y\log_3(3)=\log_3(x)

\text{but }\,\log_3(3)=1, \text{so,}

y=\log_3(x)



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