Category: Logarithms

Question Number 115859 by bemath last updated on 29/Sep/20 $$Determine,insimplestformthe$$$$smallestofthethreenumbersx,$$$$yandzwhichsatisfythesystem$$$$$$\{\begin{array}{l}\log {}_9\left(x\right)+\log {}_9\left(y\right)+\log {}_3\left(z\right)=2\\ \log {}_{16}\left(x\right)+\log {}_4\left(y\right)+\log {}_{16}\left(z\right)=1\\ \log {}_5\left(x\right)+\log {}_{25}\left(y\right)+\log {}_{25}\left(z\right)=0\end{array}$$…

Question Number 181154 by mathlove last updated on 22/Nov/22 $${\left({log}_{15}5\right)}^2+\left({log}_{15}3\right)\left({log}_{15}75\right)=?$$$$$$ Answered by SEKRET last updated on 22/Nov/22…

Question Number 115341 by bemath last updated on 25/Sep/20 $$If\log \tan 1°+\log \tan 2°+\log \tan 3°+\dots +\log \tan 89°=p$$$$then{p}^2+3=$$ Answered by bobhans last updated on 25/Sep/20 $$\Rightarrow \log (\tan 1°\times \tan 2°\times \tan 3°\times \dots \times \tan 89°)=p$$$${consider}\:\mathrm{tan}\:\mathrm{89}°×\mathrm{tan}\:\mathrm{1}°=\mathrm{1}…

Question Number 115246 by bemath last updated on 24/Sep/20 $$5^{{(x+1)}^2}+625⩽5^{x^2+2}+5^{2x+3}$$ Commented by bobhans last updated on 24/Sep/20 $${let}\:\mathrm{5}^{{x}^{\mathrm{2}} }…

Question Number 49691 by Rio Michael last updated on 09/Dec/18 $$simplify\frac{{log}_{3}64\times {log}_{4}243}{{log}_{2}16}$$ Answered by math1967 last updated on 09/Dec/18 $$\frac{{log}_{\mathrm{3}} \mathrm{4}^{\mathrm{3}}…