Respuesta :

[tex]\bf \textit{logarithm of factors}\\\\ log_a(xy)\implies log_a(x)+log_a(y) \\\\\\ \textit{Logarithm of rationals}\\\\ log_a\left( \frac{x}{y}\right)\implies log_a(x)-log_a(y)\\\\ -------------------------------\\\\ log_5(2)+log_5(10)-log_5(4)\implies log_5(2)+\left[log_5\left( \cfrac{10}{4} \right) \right] \\\\\\ log_5(2)+log_5\left( \cfrac{5}{2} \right)\implies log_5\left[(2)\left( \frac{5}{2} \right) \right]\implies log_5(5)\implies 1[/tex]
shubhamchouhanvrVT

The solution to the expression log₅ ( 2 )+ log₅( 10 ) - log₅( 4 ) is 1. Option B is correct.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression is calculated as:-

E = log₅ ( 2 )+ log₅( 10 ) - log₅( 4 )

Use Logarithmic property Loga(x / y ) = Loga(x) - Loga(y)

E = log₅ ( 2 ) + log₅( 10 / 4 )

Use Logarithmic property Loga(x y ) = Loga(x) + Loga(y)

E = log₅  [ 2 x ( 10 / 4 ) ]

E =   log₅ ( 5 ) = 1

Therefore, the solution to the expression log₅ ( 2 )+ log₅( 10 ) - log₅( 4 ) is 1. Option B is correct.

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