Question

The number of solution of
$log_{16}(x)$
=
$log_{4}(x - 2)$
is? Can anyone EXPLAIN this answer please? I need it now
​

Answer 1

Answer:

2

Step-by-step explanation:

First you should know the change of base rule:

$log_{b}(x) = \frac{ log_{a}(x) }{ log_{a}(b) }$

log16 (x) = log4 (x) / log4 (16)

= log4 (x) / 2

= log4 (✓x)

The question can be rewritten as:

log4 (√x) = log4 (x-2)

Taking antilog on both sides,

✓x = x-2

Squaring on both sides,

x = (x-2)²

x = x² + 4 - 2x

x²-3x+4=0

Which is quadratic eqn with 2 roots

Therefore the number of solutions = 2