Ask Me Help Desk - Logarithmic functions 2

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Logarithmic functions 2

I really need help espeically on this one
Any help would be appreciated

File attachment of equation below thanks

Okay, what do you want to do with the equation?

Is that log base 10 or log of 10? Are the fractions meant to be powers?

Sorry they are
Log of base 10 and they are just normal fractions

Since you haven't told me what you're aiming to do, I'll guess that you want to format it into a single number.
Here you can make use of a property of logarithms:

$log(A)+log(B) = log(AB)$

This works as long as the logs are in the same base, as is the case here.

Then you should be able to simplify the term inside the log, probably.

My assignment asks me to simplify the question

I just don't know how to mutiply the numerator with the other numerator due to a square root being there

$log_{10}((\frac{1}{2}+\frac{\sqrt{5}}{2})(\frac{3} {2}+\frac{\sqrt{5}}{2}))$

$log_{10}((\frac{1}{2}\frac{3}{2})+(\frac{\sqrt{5}} {2}\frac{\sqrt{5}}{2})$ $+(\frac{\sqrt{5}}{2}\frac{3}{2})+(\frac{1}{2}\frac {\sqrt{5}}{2}))$

$log_{10}((\frac{3}{4})+(\frac{5}{4})+(\frac{3\sqrt {5}}{4})+(\frac{\sqrt{5}}{4}))$

$log_{10}(\frac{3+5+3\sqrt{5}+\sqrt{5}}{4})$

$log_{10}(\frac{8+4\sqrt{5}}{4})$

This is all very very simple stuff, you should be able to do it yourself. The square root operations are basically the same for any other number, I know they look awkward but there's really no need to be scared of them.

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