Skip to content

Quant · Algebra

Logarithms

4 sub-topics · 32 lessons · 90 questions · 24 PYQs

Videos are being made — every lesson's notes and practice are ready now.

Log Laws and Evaluation12 lessons · 32 questions · 7 PYQs

What this sub-topic covers

Logarithmic Equations8 lessons · 21 questions · 7 PYQs

What this sub-topic covers

Logarithmic Inequalities7 lessons · 21 questions · 5 PYQs

What this sub-topic covers

Logarithms with Progressions5 lessons · 16 questions · 5 PYQs

What this sub-topic covers

Formula sheet

Log with a squared base
$\log_{(x^2)}y=\tfrac12\log_x y$
Log of a square keeps both signs
$\log_b\left(X^2\right)=2\log_b|X|$
Smaller base, larger log
$x>1,\ a,b>1:\ \log_ax>\log_bx\iff a<b$
A log plus its reciprocal equals 2
$\log_x y+\log_y x=2\iff x=y\ (x,y>0,\ne1)$
Chain rule for logs
$\log_a b\cdot\log_b c\cdot\log_c d=\log_a d$
Sum of reciprocal logs
$\frac1{\log_a N}+\frac1{\log_b N}=\log_N(ab)$
A log in the exponent
$a^{\log_a N}=N,\quad a^{\log_b c}=c^{\log_b a}$
Log inequality with base greater than 1
$a>1:\ \log_a X<k\iff 0<X<a^k;\quad \log_a X>k\iff X>a^k$