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AP TET Paper 2 Math and Science Model Paper 2

Question : 99 of 150

Marks: +1, -0

log (x + 3) + log (x + 5) = log 35, solve for x :

Solution:

Concept:

Use the product rule of logarithms:

\log a + \log b = \log(ab)

. If

\log A = \log B

, then

A = B

Explanation:

Given:

\log(x+3) + \log(x+5) = \log 35

Apply the product rule:

\log[(x+3)(x+5)] = \log 35

Since the logarithms are equal, their arguments must be equal:

(x+3)(x+5) = 35

Expand:

x^2 + 8x + 15 = 35

Rearrange:

x^2 + 8x - 20 = 0

Factorize:

(x+10)(x-2) = 0

So,

x = -10

x = 2

Check the domain:

x+3 > 0

and

x+5 > 0

, so

x > -3

Thus,

x = -10

is invalid because

\log(-7)

and

\log(-5)

are undefined.

Therefore, the valid solution is

x = 2

Answer:

x = 2

, which is option B.

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