Question

If x=log 3 base 2 and y=log5 base 2
Find log7.5 base 2 in terms of x and y

Answer 1

Answer:

Step-by-step explanation:

x = log 3 base 2 , y = log 5 base 2

x + y = log 15 base 2

x + y - 1  = log 15 base 2 -  log 2 base 2  , 1 = log2 base 2

x + y -1 = log (15÷2) base 2

log 7.5 base 2 = x + y - 1

Answer 2

Given,

x = log 3 base 2

y = log 5 base 2

To find,

The value of log 7.5 base 2, in terms of x and y.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

I) log A base c + log B base c = log (A×B) base c

II) log A base c - log B base c = log (A/B) base c

III) log c base c = 1

{Equation-1}

Now, according to the question;

log 3 base 2 = x

log 5 base 2 = y

On adding both the given equations, we get;

log 3 base 2 + log 5 base 2 = (x+y)

=> log (3×5) base 2 = (x+y)

log (3×5) base 2 = (x+y) {according to the equation-1 (I)}

=> log (15) base 2 = (x+y)

=> log (7.5×2) base 2 = (x+y)

=> (log 7.5 base 2) + (log 2 base 2) = (x+y)

{according to the equation-1 (I)}

=> (log 7.5 base 2) + 1 = (x+y)

{according to the equation-1 (III)}

=> log 7.5 base 2 = x+y-1

Hence, the value of log 7.5 base 2 is equal to (x+y-1).