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 65934 by gunawan last updated on 06/Aug/19

$${\log }_{7}2=a$$$${\log }_{2}3=b$$$${\log }_{6}98=...$$

Answered by meme last updated on 06/Aug/19

$$answers$$$${log}_{7}2=\frac{ln2}{ln7}=0.35=a$$$${log}_{2}3=\frac{ln3}{ln2}=1.58=b$$$${log}_{6}98=\frac{ln98}{ln6}=2.55$$

Answered by Kunal12588 last updated on 06/Aug/19

$${log}_{6}98={log}_6\left(2\times 7^2\right)$$$$={log}_{6}2+2{log}_{6}7$$$$=\frac{{log}_{7}2}{{log}_7\left(2\times 3\right)}+\frac{2{log}_{2}7}{{log}_{2}2+{log}_{2}3}$$$$=\frac{a}{a+{log}_{7}3}+\frac{2\times \frac{{log}_{7}7}{{log}_{7}2}}{1+b}$$$$=\frac{a}{a+\frac{{log}_{2}3}{{log}_{2}7}}+\frac{2}{a(1+b)}$$$$\Rightarrow \frac{a}{a+ab}+\frac{2}{a+ab}$$$$\Rightarrow \frac{a+2}{a+ab}$$

Answered by Kunal12588 last updated on 06/Aug/19

$${log}_{7}2=\frac{ln2}{ln7}=a$$$${log}_{2}3=\frac{ln3}{ln2}=b$$$${log}_{6}98=\frac{ln2+2ln7}{ln2+ln3}$$$$=\frac{\frac{ln2}{ln2}+\frac{2ln7}{ln2}}{\frac{ln2}{ln2}+\frac{ln3}{ln2}}$$$$=\frac{1+\frac{2}{a}}{1+b}$$$$=\frac{a+2}{a+ab}$$

Commented by gunawan last updated on 06/Aug/19

$$\mathrm{thank}\mathrm{you}\mathrm{Sir}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com