Logarithmic expressions Questions with solutions

The logarithmic expressions by simplifying with logarithmic identities is one type of log problems in mathematics. The worksheet of practice questions on simplifying the logarithm expressions with answers is given here for students and solutions to learn how to find the values of log expressions by simplification using logarithmic rules.

Arithmetic form

$(1).\,\,$ Evaluate $\log_{5}{7^{\displaystyle -3\log_{7}{5}}}$

$(2).\,\,$ Evaluate $7\log_{2}{\bigg(\dfrac{16}{15}\bigg)}$ $+$ $5\log_{2}{\bigg(\dfrac{25}{24}\bigg)}$ $+$ $3\log_{2}{\bigg(\dfrac{81}{80}\bigg)}$

$(3).\,\,$ Evaluate $\log_{\sqrt{2}}{\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}}}$

Algebraic form

$(1).\,\,$ Evaluate $\log{\dfrac{x^2}{yz}}$ $+$ $\log{\dfrac{y^2}{zx}}$ $+$ $\log{\dfrac{z^2}{xy}}$

$(2).\,\,$ Evaluate $\dfrac{1}{\log_{\large ab}{abc}}$ $+$ $\dfrac{1}{\log_{\large bc}{abc}}$ $+$ $\dfrac{1}{\log_{\large ca}{abc}}$

$(3).\,\,$ Evaluate $\log_{\large a}{x}$ $+$ $\log_{\large a^2}{x^2}$ $+$ $\log_{\large a^3}{x^3}$ $+$ $\cdots$ $\log_{\large a^n}{x^n}$

Trigonometric form

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.