Question and Answers Forum

All Questions      Topic List

Logarithms Questions

Previous in All Question      Next in All Question      

Previous in Logarithms      Next in Logarithms      

Question Number 182632 by cortano1 last updated on 12/Dec/22

$$\mathrm{If}\log {}_{11}\left(3\mathrm{p}\right)=\log {}_{13}(\mathrm{q}+6\mathrm{p})=\log {}_{143}\left({\mathrm{q}}^2\right)$$$$\mathrm{find}\frac{\mathrm{p}}{\mathrm{q}}.$$

Answered by manxsol last updated on 12/Dec/22

$$3p={11}^k$$$$q+6p={13}^k$$$$q^2={11}^k.{13}^k$$$$.................$$$$q^2=3p(q+6p)$$$$q^2=3pq+18p^2$$$$1=3\left(\frac{p}{q}\right)+18{\left(\frac{p}{q}\right)}^2\frac{p}{q}=x$$$$18x^2+3x-1=0$$$$(6x-1)(3x+1)=0$$$$\frac{p}{q}=\frac{1}{6}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com