Question

If log√27 x= 5 1/3,the value of x is:(where log=0.4771)

Answer 1

$log( \sqrt{27}x) = 5 \frac{1}{3} \\ log(3x) = \frac{16}{3} \\ log(3) + log(x) = \frac{16}{3} \\ log(x) = \frac{16}{3} - log(3) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 5.3333 - 0.4771 = 4.8562$

Answer 2

Given:

log√27 x= 5 1/3

To Find:

The value of x

Solution:

log√27 x = $log(27x)^{1/2}$

                =1/2×(log27x)    (∴ $logb^{a} = alogb$ )

                 =1/2(log27+logx)  (∴$logab = loga+ logb$)

                 =1/2(log3³+logx)

                 =1/2(3log3+logx)

                 =(3/2log3)+(1/2logx)

                =0.705+1/2logx

According to question

log√27 x= 5 1/3

⇒0.705+1/2logx = 16/3

⇒0.705+1/2logx = 5.33

⇒1/2logx = 4.625

⇒logx = 9.25      

⇒x = $10^{9.25}$

Hence, the value of x  is  $10^{9.25}$