Question

. If log(x-2) + log(x-3) = log 2 then the values of x are *

a..2,3

b..1,2

c..1,4

d..3,4​

Answer 1

Question :

If log(x-2) + log(x-3) = log 2 then the values of x are *

a.2,3

b.1,2

c.1,4

d.3,4

Solution :

log(x-2) + log(x-3) = log2

$\tt \implies$ log(x-2)(x-3) = log2

$\tt \implies$ (x-2)(x-3) = 2

$\tt \implies$ x² - 2x - 3x + 6 = 2

$\tt \implies$ x² - 5x + 6 - 2 =0

$\tt \implies$ x² - 5x + 4 = 0

$\tt \implies$ x² - 4x - x + 4 = 0

$\tt \implies$ x(x-4) - 1(x-4) = 0

$\tt \implies$ (x-4)(x-1) = 0

$\tt \implies$ x = 4 or x = 1

x = 1 , 4

Option :

The correct option is option c.

Properties of logarithm

● loga + logb = logab

● loga - logb = loga/b

● log 1 = 0

● log 0 = not defined

● $\tt log{a}^{b} = bloga$

● $\tt {log}_{a}{a} = 1$