Find the value of log4 6425616 Find the logarithm of 4 squar

Find the value of log_4 64.256/16 Find the logarithm of (4, square root 4, cube root 4, 4) base 2. Prove the product property of logarithms, log m/n = log m - log_b n, using the properties of exponents.

Solution

11. log4( 64*256/16)

= log4( 4*256)

=log4(4*4^4)

=log4(4^5)

Using the log property : log(a^x) = x*loga

= 5(log₄4)

= 5(1)

=5

Option C

12. log2( 4 . sqrt4. 4^1/3. 4^1/4)

=log2( 4^(1+1/2+1/3+1/4))

= log2( 4^( 12+6+4+3)/12)

= log2(4^25/12)

= log2(2^2(^25/12))

= log2( 2^(25/6))

=log2(2^(25/6))

Now we know : log_xx = logx/logx =1

=log2(2^(25/6))

= (25/6) log₂2

= 25/6

Option E