Question

evaluate log2 45 as product of X and Y if X=log2 3 and Y=log2=5​

Answer 1

Answer:

Logarithm Calculator log(x)

with b being the base, x being a real number, and y being an exponent. For example, 23 = 8 ... log2(8) = 3 (log base 2 of 8) The exponential is 23 =

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ X = log_{2}(3) \: \: and \: \: Y = log_{2}(5) }$

TO DETERMINE

$\displaystyle \sf{ log_{2}(45) \: \: in \: terms \: of \: X \: and \: Y }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on logarithm that

$\sf{1. \: \: \: log( {a}^{n} ) = n log(a) }$

$\sf{2. \: \: log(ab) = log(a) + log(b) }$

$\displaystyle \sf{3. \: \: log \bigg( \frac{a}{b} \bigg) = log(a) - log(b) }$

$\sf{4. \: \: log_{a}(a) = 1}$

EVALUATION

Here it is given that

$\displaystyle \sf{ X = log_{2}(3) \: \: and \: \: Y = log_{2}(5) }$

Now

$\displaystyle \sf{ log_{2}(45) }$

$\displaystyle \sf{ = log_{2}( {3}^{2} \times 5) }$

$\displaystyle \sf{ = log_{2}( {3}^{2} ) + log_{2}(5) }$

$\displaystyle \sf{ = 2 log_{2}( {3}^{} ) + log_{2}(5) }$

$\displaystyle \sf{ = 2 X + Y }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ if 2log x base y=6,then the relation between x and y

https://brainly.in/question/27199002

2.If 2log((x+y)/(4))=log x+log y then find the value of (x)/(y)+(y)/(x)

https://brainly.in/question/24081206