Question

¼ log b x – 2 log b 5 – 10log b y

Answer 1

I will leave out the base, b since it's the same for all these logarithms.

$\frac{1}{4} Log(x)-2Log(5)-10Log(y) \\ \\ Power-Rule \\ \\ Log( x^{ \frac{1}{4} } )-Log( 5^{2} )-Log( y^{10} ) \\ \\ Quotient-Rule \\ \\ Log( x^{ \frac{1}{4} } ) -Log( \frac{25}{ y^{10} } ) \\ \\ Quotient-Rule \\ \\ Log( \frac{ x^{ \frac{1}{4} } y^{10} }{25} )$