Logarithmic expressions

An expression that expresses a quantity in logarithmic form is called a logarithmic expression.

Introduction

The quantities are expressed mathematically in logarithmic form in some cases. Actually, a logarithmic expression is used to represent either a known quantity or an unknown quantity in mathematical form.

A logarithmic expression can represent a quantity in one term or two or more terms connected by the plus or minus or combination of both symbols.

Known quantity

The following five example mathematical expressions are the logarithmic expressions, which represent the known quantities.

$(1).\,\,\,$ $\log_{7}{(343)}$

$(2).\,\,\,$ $\log_{2}{(\log_{2}{4})}$

$(3).\,\,\,$ $2^{\displaystyle \log_{3}{(5)}}-5^{\displaystyle \log_{3}{(2)}}$

$(4).\,\,\,$ $\dfrac{1}{3}\log{27}+2\log{\Big(\dfrac{1}{3}\Big)}$

$(5).\,\,\,$ $\log_{3}{(1)}+\log_{5}{(2)}-\log_{7}{(3)}$

Unknown quantity

The following five example mathematical expressions are the logarithmic expressions, which represent the unknown quantities.

$(1).\,\,\,$ $\log_{6}{(y)}$

$(2).\,\,\,$ $4-\log{(x+1)}$

$(3).\,\,\,$ $\log_2{\Big(\log_3{\Big(\log_4{(z)}\Big)}\Big)}$

$(4).\,\,\,$ $\log_5{x}$ $+$ $\log_x{5}$

$(5).\,\,\,$ $\log_a{\Bigg(1-\dfrac{1}{2}\Bigg)}$ $+$ $\log_a{\Bigg(1-\dfrac{1}{3}\Bigg)}$ $-$ $\log_a{\Bigg(1-\dfrac{1}{5}\Bigg)}$

Problems

The list of log expression problems with solutions to learn how to evaluate or simplify the logarithmic expressions in different methods.