Question

If log₁₀ x = y, then log₁₀³ x² equals
(a) 1/3 y (b) 2/3 y (c) 3/2 y (d) 3 y

Answer 1

$\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}$

Actually Welcome to the Concept of the Logarithms.

Now basically here, we are going to use the

identities like,

1.) Log (m^n) = n Log (m)

2.) Log base (a^b) = 1/b* Log base ( a)

so applying these we get as,

here,

=> Log (x) base 10 = y ..... (3)

so we get as,

=> Log (x) ^2 base (10) ^3 = 2*Log (x) base (10) ^3

in the next steps, applying the identity.. (2) we get as,

=> 2/3 * Log(x) base (10)

from... (3) , we write as,

=> 2/3 *yso finally we get as

=> 2/3 y

⭐the correct option is "b"