Math Doubts

Logarithmic equations worksheet

Test your skill on logarithms by solving following logarithmic equations and check your answer with our solution for improving your knowledge on solving logarithmic equations mathematically.

$(1) \,\,\,\,\,\,$ $\log_{3}{(5x-2)}$ $-$ $2\log_{3}{\sqrt{3x+1}}$ $=$ $1-\log_{3}{4}$

$(2) \,\,\,\,\,\,$ $\dfrac{\log_{2}{(9-2^x)}}{3-x}$ $\,=\,$ $1$

$(3) \,\,\,\,\,\,$ $2\log_{2+\sqrt{3}} {(\sqrt{x^2+1}+x)}$ $\,+\,$ $\log_{2-\sqrt{3}} {(\sqrt{x^2+1}-x)}$ $\,=\,$ $3$

$(4) \,\,\,\,\,\,$ $\log_{x} 2 \times \log_{\frac{x}{16}}{2}$ $\,=\,$ $\log_{\frac{x}{64}}{2}$

$(5) \,\,\,\,\,\,$ $2\log_{x}{a}$ $+$ $\log_{ax}{a}$ $+$ $3\log_{a^2x}{a}$ $\,=\,$ $0$

$(6) \,\,\,\,\,\,$ $x+\log{(1+2^x)}$ $\,=\,$ $x\log{5}$ $+$ $\log{6}$

$(7) \,\,\,\,\,\,$ $x^{(\log_{2}{x})+4} \,=\, 32$

$(8) \,\,\,\,\,\,$ $x^{(\log_{2}{x})+4} \,=\, 32$

$(9) \,\,\,\,\,\,$ $\log_{5-x}{(x^2 -2x+65)}$ $\,=\,$ $2$

$(10) \,\,\,\,\,\,$ $\log_{5}{x}$ $+$ $\log_{x}{5}$ $\,=\,$ $\dfrac{5}{2}$

$(11) \,\,\,\,\,\,$ $\dfrac{x}{y}$ $+$ $\dfrac{y}{x}$ If $\log \Bigg[\dfrac{x+y}{3}\Bigg]$ $\,=\,$ $\dfrac{1}{2} (\log x + \log y)$

$(12) \,\,\,\,\,\,$ $\dfrac{\log(\sqrt{x+1}+1)}{\log \sqrt[3]{x-40}}$ $\,=\,$ $3$

$(13) \,\,\,\,\,\,$ $\log_{10} \Big[98$ $+$ $\sqrt{x^2-12x+36}\Big]$ $\,=\,$ $2$

$(14) \,\,\,\,\,\,$ $\log_{2}{x}$ $+$ $\log_{4}{x}$ $+$ $\log_{16}{x}$ $\,=\,$ $\dfrac{21}{4}$

$(15) \,\,\,\,\,\,$ $\log{7}$ $+$ $\log{(3x-2)}$ $\,=\,$ $\log{(x+3)}+1$



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