Question

if 3 log (x+3)=log27then the value of x is
a.0
b.1
c.6
d.24​

Answer 1

Given:

• 3log(x+3)= log27

To Find:

• Value of x for the given equation

Solution:

We know that,

$\rightarrow\bf{a\:log_{m}b=log_{m}b^{a},where\:m>0,m\neq1,b>0}$

$\rightarrow\bf{If\:log_{m}a=log_{m}b,then\:a=b,where\:m>0,m\neq1,a>0,b>0}$

$\rightarrow\bf{\sqrt[3]{27}=3}$

Now,

↬ 3log(x+3)= log27

↬ log(x+3)³= log27

↬ (x+3)³= 27

↬ x+3= ∛27

↬ x+3= 3

↬ x= 3-3

↬ x= 0

Hence, the value of x is 0(option a).

Answer 2

Answer:

a. 0

Step-by-step explanation:

Given:

3 log (x+3) = log 27

To find:

Value of x

Solution:

$3 \log(x + 3)= \log \: 27 \\ 3 \log {(x + 3)} = \log {3}^{3} \\ 3 \log(x + 3) = 3 \log3$

[Cancelling the 3 log from both side]

$x + 3 = 3 \\ x = 3 - 3 \\ x = 0$

Hence, the required answer is 0.

The correct option is a .

Using formula

2 log 3 = log 3²

log 2 = log 3 $\implies$ 2 = 3