Category: Logarithms

Question Number 179679 by ROOSEVELT last updated on 01/Nov/22 $${\int }_2^4\tan \left(x\right)$$ Answered by Acem last updated on 01/Nov/22 $${a}=\:−\mathrm{ln}\:\mid\mathrm{cos}\:{x}\mid\:\mid_{\mathrm{2}} ^{\mathrm{4}} \:=\:−\mathrm{ln}\:\mid\mathrm{cos}\:\mathrm{4}\mid+\:\mathrm{ln}\:\mid\mathrm{cos}\:\mathrm{2}\mid \…

Question Number 113862 by Aina Samuel Temidayo last updated on 15/Sep/20 Answered by 1549442205PVT last updated on 16/Sep/20 $$\mathrm{From}\mathrm{the}\mathrm{hypotesis}\mathrm{we}\mathrm{have}$$$$\frac{\mathrm{logx}}{\mathrm{b}-\mathrm{c}}=\frac{\mathrm{logy}}{\mathrm{c}-\mathrm{a}}=\frac{\mathrm{logz}}{\mathrm{a}-\mathrm{b}}=\mathrm{k}.\mathrm{Hence},\mathrm{we}\mathrm{get}$$$$\{\begin{array}{l}\mathrm{logx}=\mathrm{k}(\mathrm{b}-\mathrm{c})\\ \mathrm{logy}=\mathrm{k}(\mathrm{c}-\mathrm{a})\\ \mathrm{logz}=\mathrm{k}(\mathrm{a}-\mathrm{b})\end{array}$$$$\mathrm{Adding}\:\mathrm{up}\:\mathrm{three}\:\mathrm{equalities}\:\mathrm{we}\:\mathrm{obtain}…

Question Number 113800 by Aina Samuel Temidayo last updated on 15/Sep/20 $$\log \left(\mathrm{ab}\right)-\log \mid \mathrm{b}\mid =$$$$$$$$\mathrm{A}.\log \left(\mathrm{a}\right)\mathrm{B}.\log \mid \mathrm{a}\mid \mathrm{C}.-\log \left(\mathrm{a}\right)\mathrm{D}.$$$$\mathrm{None}\mathrm{of}\mathrm{these}.$$ Answered by MJS_new last updated…

Question Number 48202 by F_Nongue last updated on 20/Nov/18 $$howcanIgetthex?$$$$a)3^x+4^x=5^x$$$$b)7^{6-x}=x+2$$$$c){\left(\sqrt{2+\sqrt{3}}\right)}^x+{\left(\sqrt{2-\sqrt{3}}\right)}^x=2^x$$$$\left.{d}\right)\mathrm{3}^{{x}−\mathrm{2}} =\frac{\mathrm{9}}{{x}} \…

Question Number 112808 by Aina Samuel Temidayo last updated on 09/Sep/20 Answered by 1549442205PVT last updated on 10/Sep/20 $$\mathrm{We}\mathrm{have}{\log }_2(10+2\mathrm{x})={\log }_{10}(\mathrm{x}-4)+2$$$$\Leftrightarrow\left[\mathrm{log}_{\mathrm{2}} \left(\mathrm{10}+\mathrm{2x}\right)−\mathrm{2}\right]−\mathrm{log}_{\mathrm{10}} \left(\mathrm{x}−\mathrm{4}\right)=\mathrm{0}\left(\mathrm{1}\right)…