Question

Given that x=log3 base 2 and y=log5 base 2 then log 6750 base 2 value in the term of x. and y.​

Answer 1

Answer:

1 + 3x + 3y

Step-by-step explanation:

x = log 3 to the base 2

y = log 5 to the base 2

Now 6750 = 2 × 3³ × 5³

Hence

Log 6750 to base 2 can be written as

Log 2 × 3³ × 5³ to base 2

= log 2 to base 2 + log 3³ to base 2 + log 5³ to base 2

(using property log mn = log m + log n)

= 1 + 3log 3 to base 2 + 3log 5 to base 2

(using properties log a to base a = 1, and log m raise to power n = nlog m)

Now substituting values of x and y we get

= 1 + 3x + 3y