Logarithms

• Logarithm is a degree, to which you need to pow a number to.
• The difference of logarithms with the same base is equal to the logarithm of the quotient

  $log_{a}x-log_{a}y=$$log_{a}\frac{x}{y}, a,b,c>0,a\neq1$
• Main logarithmic rule:

  $a^{log_ab}=$$b$
• Logarithm of the product is equal to the sum of logarithms from each of the co-dominants

  $\log_a{}(b*c)=$$\log_ab+$$\log_a{c}$
• Logarithm of a number in power is equal to the multiplication of power number and logarithm of a number without power:

  $\log_ab^c=$$c\log_ab$
• Logarithm of a number with base in power is equal to the logarithm with the same base, but divided by the power of the base

  $\log_{a^c}b=$$\frac{\log_ab}{c} =$$\frac{1}{c}\log_ab$
• Transition to a new base:

  $log_a{b}=$$\frac{\log_cb}{\log_ca}$