log 2 (x) + log 2 (5)= log 2 10

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

log 2 (X) + log 2 (5) = log 2 (10)

We know that :

log x + log y = log xy

==? log 2 (5*x) = log 2 (10)

==> log 2 (5x) = log 2 (10)

==> 5x = 10

==> x= 10/5 = 2

==> x= 2

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

log2 (x) +log2 (5) = log2 (10).

Solution:

log2(x)+log(5) = log2(10)

log2(x*5) = log2(10), as log a(x)+loga(y) = loga(x*y).

Since the logarithm bases are same on both sides, we take antilogarithms on both sides:

5x = 10

5x/5 = 10/2

x =2.

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