Question

Solve for n

Answer 1

\[\log_{9}27=n \]

Answer 2

n is already isolated. Did you mean simplify?

Answer 3

probably means find the value of \(n\) that makes this true...

Answer 4

\[\log_b a =n \] means the number \(n\) is the power you have to raise \(b\) to in order to get \(a\)

so for example \[\log_{10} 1000 = 3\]because \[10^3=1000\]

Answer 5

hint: this problem will involve a fractional power, so it may be helpful to remember that \[n^{a/b} = \sqrt[b]{n^a}\]

Answer 6

This simply means 9^n = 27
(3^2)^n = 27 = 3^3
so 3^2n = 3^3 and 2n = 3 giving n = 3/2

Or you can maintain the log but change the term within as follows...
\[\log_9 27 = \log_9 3^3 = 3 \log_9 3 = 3 \log_9 \sqrt{9} = 3 \log_9 (9)^{0.5} = \frac{ 3 }{ 2 } \log_9 9 = \frac{ 3 }{ 2 }\]

Answer 7

An alternative approach is to change the base to a nicer one, say base 3 rather than base 9 and this gives the answer very directly!
Use this change base rule:
\[\log_ab= \frac{ \log_cb }{ \log_ca }\]

So \[\log_927 = \frac{ \log_3 27 }{ \log_39 }=\frac{ 3 }{ 2 }\]

Answer 8

please close this question if your finished getting help

Answer 9

also, if you are allowed to use a calculator, you can do
\[ \log_9 27= \frac{\log 27}{\log 9 } \]
where log means log base 10 (the one your calculator uses)