Question

Find the value of x in {log(8) to the base 27} * {log(3) to the base x) =1
Select one:
O a. 1
b. 1/3
O c.-3
d. 2​

Answer 1

Step-by-step explanation:

c- 3 is the answer of your questions

Answer 2

Answer:

D. The value of x is 2.

Step-by-step explanation:

Given: $(log_{27} 8) (log_{x} 3) = 1$

To find: The value of x.

Solution:

This can be solved by using the Change of Base concept, which is stated below:

$log_{a}x . log_{b} y= \frac{log x}{log a} . \frac{log y}{log b}$

Putting the above formula in the given question, we get,

$\frac{log 8}{log 27} . \frac{log 3}{log x} = 1$

27 can be written as $3^{3}$.

$\frac{log 8}{log 3^{3} } . \frac{log 3}{log x} = 1$

Using $logx^{a} = alogx$, we get

$\frac{log 8}{3 log 3} . \frac{log 3}{log x} =1$

Log3 in the numerator gets cancelled with Log3 in the denominator.

Now, we are left with,

$\frac{log8}{3} . \frac{1}{logx} =1$

8 can be written as $2^{3}$.

$\frac{log 2^{3} }{3 logx } = 1$

3log 2 = 3log x

3 is cancelled both sides,

log 2 = log x

Therefore, x = 2 is the correct option.