# 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.

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