Question

find x of log2 4x= 5​

Answer 1

Answer:

in a variety of ways

for example

log

2

(

4

x

)

=

5

⇒

log

2

4

+

log

2

x

=

5

⇒

2

+

log

2

x

=

5

⇒

log

2

x

=

3

⇒

x

=

2

3

=

8

OR

log

2

(

4

x

)

=

5

2

log

2

(

4

x

)

=

2

5

4

x

=

32

x

=

8

OR

simplest, maybe, taken straight from the idea that a logarithm is just an index

log

2

(

4

x

)

=

5

⇒

4

x

=

2

5

⇒

x

=

2

5

⋅

2

−

2

=

2

3

=

8

please mark a brilliant

Answer 2

Given :

$\sf log_{2}(4x) = 5$

To find :

• the value of x

Solution :

$\sf \implies log_{2}(4x) = 5$

We know that :-

$\sf if \: log_{a}(b) = n \\ \sf then \: \: b = {a}^{n}$

$\sf \implies (4x) = {(2)}^{5}$

4 = 2²

$\sf \implies {2}^{2} \: x= {(2)}^{5}$

$\sf \implies x= \dfrac{{(2)}^{5} }{{(2)}^{2} }$

We know that :-

$\boxed{\bf \dfrac{{(a)}^{m} }{{(a)}^{n} } = {a}^{m - n} }$

$\sf \implies x= {{(2)}^{5 - 2} }$

$\sf \implies x= {(2)}^{3}$

$\sf \implies x= 2 \times 2 \times 2$

$\sf \implies x= 8$

Answer :

• value of x = 8