Logarithm solving problem: Log(8) + Log(x) = 6 Log (5)

[HarveySpecter]

Hello,

I got a exercise which is breaking my mind right now,

Log(8) + Log(x) = 6 Log (5)

It seems simple but I'm just not getting my head around this.
I am supposed to answer it in it's exact form so no decimals.

Anyone who can help me to get to that X without solving the Logs to decimal numbers?

And if you know a good page which explains this problem whould also be really handy
to get because I was not able to learn it from my teacher or any other student for that instance.

 

[tkhunny]

Hello,

I got a exercise which is breaking my mind right now,

Log(8) + Log(x) = 6 Log (5)

It seems simple but I'm just not getting my head around this.
I am supposed to answer it in it's exact form so no decimals.

Anyone who can help me to get to that X without solving the Logs to decimal numbers?

And if you know a good page which explains this problem whould also be really handy
to get because I was not able to learn it from my teacher or any other student for that instance.

Please use the basic rules of logarithms.

\(\displaystyle \log(a) + \log(b) = \log(a\cdot b)\)

\(\displaystyle a\cdot\log(b) = \log\left(b^{a}\right)\)

 

[HallsofIvy]

And the fact that "logarithm" is a one-to-one function: if log(x)= log(y) then x= y.