Question

If x= log 3 base 2 and y= log 5 baae 2 then the value of log (1125) base 2 in terms of x and y

Answer 1

Step-by-step explanation:

answer is in the above picture

Answer 2

Answer:

Required value of $log_{2}(1125)$ in the term of x and y is (2x+3y)

Step-by-step explanation:

Here given

$x = log_{2}(3) \\ y = log_{2}(5)$

Here we want to find value of $log_{2}(1125)$ in terms of x and y.

By prime factorisation,

$1125 = 3 \times 3 \times 5 \times 5 \times 5 \\ = {3}^{2} \times {5}^{3}$

So,

$log_{2}(1125) = log_{2}( {3}^{2} \times {5}^{3} ) \\ = log_{2}( {3}^{2} ) + log_{2}( {5}^{3} ) \\ = 2 log_{2}(3) + 3 log_{2}(5) \\ = 2x + 3y$

Required value of $log_{2}(1125)$ in the term of x and y is (2x+3y).

Here applied formulas,

$log(a) + log(b) = log(ab) \\ log( {a}^{b} ) = b log(a)$

Some important Logarithm formulas,

$log_{x}(1) = 0 \\ log_{x}(0) = 1 \\ log_{x}(y) = \frac{ log(x) }{ log(y) } \\ log( {x}^{y} ) = y log(x) \\ log(x) + log(y) = log(xy) \\ log(x) - log(y) = log( \frac{x}{y} ) \\ log_{x}(x) = 1$

Know more about logarithm, https://brainly.in/question/21862262

https://brainly.in/question/4881267