Question

How do you expand ln(2x^2) & log2(sqrt8x^2)

Answer 1

㏑(2x²)
㏒(2x²)/㏒(e)  Change from the natural logarithm to logarithm divided by a logarithm.
2㏒(2x)/㏒(e) Change from ㏒(2x²) to 2㏒(2x)
(2㏒(2) + 2㏒(x))/㏒(e) Factor 2㏒(2x).


㏒₂(√(8x²))
㏒₂(2x√2) Change √8x² to 2x√2.
㏒₂(2x) + ㏒₂(√2) Factor ㏒₂(2x√2).
㏒₂(2) + ㏒(x) + 0.5 Change ㏒₂(2) to 0.5.
1 + ㏒(x) + 0.5 Change from ㏒₂(2) to 1.
1 + 0.5 + ㏒(x) Add 1 and 0.5.
1.5 + ㏒(x)