Question

- If log2 3 = a, then which of the following is the value of
log8 27 ?

a)3a b)1/a
c)2a d)a​

Answer 1

2^n means 2ⁿ.

Answer:

a

Step-by-step explanation:

log(2) 3 = a means 2^a = 3.

In the same way, let log(8) 27 = x, means, 8^x = 27.

On observing, 8 = 2³ & 27 = 3³, which means,

=> 8^x = 27

=> (2^3)^x = (3^3)

=> (2^x)^3= 3^3, cancel 3(power)

=> 2^x = 3 from above, 3 = 2^a

=> 2^x = 2^a

=> x = a

Answer 2

Answer:

Given :

• If log2 3 = a

To Find :

• a, then which of the following is the value of log8 27 ?

Solution :

we know that :

$: \implies \sf \: \: \: \: \: \: \: \bigg \{ log_{b}{m} = \frac{log_{a}{m}}{log_{a}{b}} \bigg \}$

Substitute all values :

$: \implies \sf \: \: \: \: \: \: \: \bigg \{ log_{8}{27} = \frac{log_{2}{27}}{log_{2}{8}} \bigg \} \\ \\ \\ : \implies \sf \: \: \: \: \: \: \: \bigg \{ log_{8}{27} = \frac{log_{2}{ {3}^{3} }}{log_{2}{ {2}^{3} }} \bigg \} \\ \\ \\ : \implies \sf \: \: \: \: \: \: \: \bigg \{ log_{8}{27} = \frac{3log_{2}{ {3}}}{3log_{2}{ {2}}} \bigg \} \\ \\ \\ : \implies \sf \: \: \: \: \: \: \: = \frac{a}{1} \\ \\ \\ : \implies \sf \: \: \: \: \: \: \: = a$

Option d is correct !