Logarithmic Expressions Questions in Algebraic form with Solutions

The logarithmic expressions are appeared in algebraic form in some questions and they should be evaluated by simplifying the algebraic based logarithmic expressions using logarithm rules. Simplifying the log expressions in algebraic form by the log identities examples worksheet is given here with answers for students to practice, and solutions to learn how to evaluate the logarithm expressions in algebraic form mathematically by the simplification.

Evaluate $\log{\dfrac{x^2}{yz}}$ $+$ $\log{\dfrac{y^2}{zx}}$ $+$ $\log{\dfrac{z^2}{xy}}$

Evaluate $\dfrac{1}{\log_{\large ab}{abc}}$ $+$ $\dfrac{1}{\log_{\large bc}{abc}}$ $+$ $\dfrac{1}{\log_{\large ca}{abc}}$

Evaluate $\log_{\large a}{x}$ $+$ $\log_{\large a^2}{x^2}$ $+$ $\log_{\large a^3}{x^3}$ $+$ $\cdots$ $+$ $\log_{\large a^n}{x^n}$

Evaluate $\dfrac{1}{\log_{2}{x}}$ $+$ $\dfrac{1}{\log_{3}{x}}$ $+$ $\dfrac{1}{\log_{4}{x}}$ $+$ $\cdots$ $+$ $\dfrac{1}{\log_{50}{x}}$

Evaluate $\dfrac{1}{\log_{\large a}{abc}}$ $+$ $\dfrac{1}{\log_{\large b}{abc}}$ $+$ $\dfrac{1}{\log_{\large c}{abc}}$