Question

evaluate log5 5√5

Answer 1

Can you express \(\large 5\sqrt5\) as just one power of 5?

Answer 2

i dont know

Answer 3

Here, two hints...first, when multiplying two factors with the same bases, just add their exponents...
\[\Large a^ma^n=a^{m+n}\]

Second, square root simply means an exponent of one half.
\[\Large \sqrt a = a^{\frac12}\]

Answer 4

ok

Answer 5

So...?
\[\huge 5\sqrt 5 = 5^{\color{red}?}\]

Finding exactly what power this is is key.

Alternatively, you can use the property involving the logarithm of a product...
\[\Large \log_b(MN)=\log_b(M) + \log_b(N)\]

Either way, it all boils down to the fact that a square root is simply an exponent of one-half.

Answer 6

ok

Answer 7

I really need you to work with me here ^_^
How do you want to go about it?
Either you express \(5\sqrt 5\) as a single power of 5, or
you can split the log into a sum of two logs as described prior.

Answer 8

i am not really sure, i just have to show how i got to the answer 3/2

Answer 9

Magic...
or...
Like I said, log(MN) = log(M) + log(N)

Can you apply that logic to \[\Large \log_5(MN) =\color{red}?\]