Category: Logarithms

Question Number 217691 by PaulDirac last updated on 18/Mar/25 Answered by mr W last updated on 19/Mar/25 $$leta=9^{9^9}$$$$I={\int }_0^{\pi }\ln \left(ax\right)dx$$$$\:\:=\frac{\mathrm{1}}{{a}}\int_{\mathrm{0}}…

Question Number 215840 by golsendro last updated on 19/Jan/25 $$\log {}_{24}3=a\mathrm{and}\log {}_{24}6=\frac{b}{6}$$$$\log {}_{\sqrt{8}}(b-4a)=?$$ Commented by oubiji last updated on 19/Jan/25 $$\:\:\:\:{b}−\mathrm{4}{a}=\mathrm{log}_{\mathrm{24}}…

Question Number 213923 by luj last updated on 21/Nov/24 Answered by MATHEMATICSAM last updated on 21/Nov/24 $$x^{32}=2^x$$$$or32\ln \mid x\mid =x\ln 2$$$$\mathrm{For}x>0$$$${or}\:\frac{\mathrm{ln}{x}}{{x}}\:=\:\frac{\mathrm{ln2}}{\mathrm{32}}\: \…

Question Number 212515 by efronzo1 last updated on 16/Oct/24 $$\mathrm{The}\mathrm{numbers}\mathrm{of}\mathrm{pairs}\mathrm{of}\mathrm{natural}$$$$\mathrm{numbers}(\mathrm{x},\mathrm{y})\mathrm{with}\mathrm{x},\mathrm{y}⩽33\mathrm{that}$$$$\mathrm{satisfy}5\mid 3^{{\mathrm{x}}^{\mathrm{y}-1}}+2^{{\mathrm{y}}^{2\mathrm{x}}}\mathrm{is}\dots$$$$\left(\mathrm{A}\right)295\left(\mathrm{B}\right)296\left(\mathrm{C}\right)297\left(\mathrm{D}\right)298\left(\mathrm{E}\right)299$$ Commented by A5T…

Question Number 211815 by alcohol last updated on 21/Sep/24 $${ax}^2+bx+c=0hasroots\alpha and\beta$$$$and\frac{\alpha }{\beta }=\frac{\lambda }{\mu }.showthat\lambda \mu b^2=ac{(\lambda +\mu )}^2$$ Answered by som(math1967) last updated on 22/Sep/24 $$\:{let}\:\alpha={k}\lambda\:,\:\beta={k}\mu \…