Question

if x = log3 base 2, y = log5 base 2 then evaluate log15 base 2 in terms of x and y.

Answer 1

Answer:

log 15 = x+y

Step-by-step explanation:

log 15= log 3×5

log m×n= log m + log n

log 3×5 = log 3 + log 5

log 15 = x+y

Answer 2

$\displaystyle \sf{ log_{2}(15) = x + y }$

Given :

$\displaystyle \sf{ log_{2}(3) = x \:, \: log_{2}(5) = y }$

To find :

The value of $\displaystyle \sf{ log_{2}(15) }$ in terms of x and y

Formula :

$\displaystyle \sf{ log_{a}(xy) = log_{a}(x) + log_{a}(y) }$

Solution :

Step 1 of 2 :

Write down the given data

$\displaystyle \sf{ log_{2}(3) = x \:, \: log_{2}(5) = y }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ log_{2}(15) }$

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

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

$\displaystyle \sf{ = x + y }$

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