Log Formula

Product Rule

• log_b(P×Q)=log_bP+log_bQ

Quotient Rule

• log_b(P/Q)=log_bP−log_bQ

Power Rule

• log_b(P^Q)=q×log_bp

Zero Rule

• log _b(1)=0

The Logarithm of a Base to a Power Rule

• log_bb^y=y

A Base to a Logarithm Power Rule

• b^logy = y

Identity Rule

• log_by=1

Basic Logarithm Formula

• log_b(m×n)=log_bm+log_bn
• log_b(m/n)=log_bm−log_bn
• log_b(x^y)=y×log_bx
• log_bm√n=log_bn^1/m
• mlog_b(x)+nlog_b(y)=log_b(x^myⁿ)

Addition and Subtraction

• log_b(m+n)=log_bm+log_b(1+n/m)
• log_b(m−n)=log_bm+log_bb(1−(n/m))
• log_nm=log_dm/log_dn