expand the given logarithm and simplify ithm and simplify So

expand the given logarithm and simplify. ithm and simplify

Solution

log_sqrt2(4x^3)

Use the log properties:

logA*B = logA +logB ; log_aB = logB/loga

Loga^x = x*loga

log_sqrt2(4x^3) = log_sqrt2(4) + log_sqrt2(x^3)

= log2^2/log(2^1/2) + logx^3/log2^1/2

= 2(log2/ 1/2log2) + 3logx/ 1/2log2

= 4(log2/log2) + 6logx/log2

= 4 + 6log₂(x)