Question

What is the value of log81 3?

Answer 1

\[\log _{81}3\]

Answer 2

There are various ways in which to do this problem.
One of the easier approaches is to re-write \[y=\log_{81} 3\] as y=\[y=\log_{3^4} 3\]. All I did here was to replace the base 81 with its equivalent as a power of 3.

Answer 3

\(\bf log_{\color{red}{ a}}{\color{blue}{ b}}=y\implies {\color{red}{ a}}^y={\color{blue}{ b}}
\\ \quad \\ \quad \\
log_{\color{red}{ 81}}{\color{blue}{ 3}}=\square \implies ?\)

Answer 4

81^y=3

Answer 5

hmm yes

Answer 6

\(\bf log_{\color{red}{ a}}{\color{blue}{ b}}=y\implies {\color{red}{ a}}^y={\color{blue}{ b}}
\\ \quad \\ \quad \\
log_{\color{red}{ 81}}{\color{blue}{ 3}}=\square \implies {\color{red}{ 81}}^y=3
\\ \quad \\
{\color{brown}{ 81\to 3\cdot 3\cdot 3\cdot 3\to 3^2\cdot 3^2\to (3^2)^2\to 3^4}}\qquad thus
\\ \quad \\
81^y=3\implies (3^4)^y=3^1\implies 3^{{\color{blue}{ 4y}}}=3^{\color{blue}{ 1}}\)

Answer 7

\(\Large\color{blue}{ \log_{81}3 }\) --> \(\Large\color{blue}{ \log_{81}81^{-1/4} }\)

Answer 8

So 3^4y = 3^1 is my answer?

Answer 9

( damn, Greece missed again.... )

Answer 10

hheh

Answer 11

\(\bf (3^4)^y=3^1\implies 3^{{\color{blue}{ 4y}}}=3^{\color{blue}{ 1}}\implies {\color{blue}{ 4y}}={\color{blue}{ 1}}\)

Answer 12

Let Solomon finish, please. He / you converted the '3' on the extreme right in to 81^(1/4), which was a clever approach. But what about the 'y' on the left side?

Answer 13

I can't finish, I am watching a match of Greece and Puerto Rice. I am like here and there....

Answer 14

Costo rico

Answer 15

Mm rice

Answer 16

OMG.... Greece couldn't finish the attack!!

Answer 17

I am out, I am commenting about soccer and shouldn't be doing that.

Answer 18

so my answer 4y=1

Answer 19

\[\large log_{81} 3 = x \Rightarrow 81^x = 3\]

Take the log of both sides
We know that \(\huge \ln(a)^b = b \times \ln(a)\) so...

\[\large x \times \ln (81) = \ln(3)\]

Divide both sides by \(\large \ln(81)\)
\[\large x = \frac{\ln(3)}{\ln(81)}\]

We find that \[\large x = 4\]

Answer 20

Note that both Solomon and Joe are attempting to convert the given problem so that both the base and the quantity of which the log is taken have the same base. If Solomon is unavailable, then Joe: would you like to guide Skittle towards finding her own answer?