For a>0, a 1, b>0 and real r, log_a(br)=rlog_a b Example log_2(5x)=xlog_2 5 log_3 2= 12log_3 2 Take note The power law applies to a power inside the logarithm. It does not make (log_a x)3=3log_a x an identity. For x>0, (log_a x)3=(log_a x)(log_a x)(log_a x)

For \(a>0,\ a\ne1,\ b>0\) and real \(r\),

The power law applies to a power inside the logarithm. It does not make \((\log_a x)^3=3\log_a x\) an identity. For \(x>0\),

\((\log_a x)^3=(\log_a x)(\log_a x)(\log_a x)\)

Exponential and Logarithmic Functions

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Power Law

Power Law