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 164806 by saboorhalimi last updated on 22/Jan/22

Commented by cortano1 last updated on 22/Jan/22

$$\log {}_{12}\left(3\right)=a\Rightarrow \log {}_3\left(12\right)=\frac{1}{a}$$$$\Rightarrow 1+2\log {}_3\left(2\right)=\frac{1}{a}$$$$\Rightarrow \log {}_3\left(2\right)=\frac{1-a}{2a}$$$$\Rightarrow \frac{\log {}_5\left(2\right)}{\log {}_5\left(3\right)}=\frac{1-a}{2a}$$$$\Rightarrow \log {}_5\left(2\right)=\left(\frac{1-a}{2a}\right)\log {}_5\left(3\right)$$$$$$

Commented by cortano1 last updated on 22/Jan/22

$$\log {}_{12}\left(3\right)=\frac{\log {}_5\left(3\right)}{\log {}_5\left(12\right)}=a$$$$\Rightarrow \log {}_5\left(3\right)=a(\log {}_5\left(3\right)+2\log {}_5\left(2\right))$$$$\Rightarrow (1-a)\log {}_5\left(3\right)=2a\log {}_5\left(2\right)$$$$\Rightarrow \log {}_5\left(2\right)=\frac{(1-a)}{2a}\log {}_5\left(3\right)$$

Commented by mr W last updated on 22/Jan/22

$$is{\log }_{5}3betterthan{\log }_{5}2?$$

Commented by cortano1 last updated on 22/Jan/22

$$yes$$

Commented by mr W last updated on 22/Jan/22

$$andhowtoget{\log }_{5}3?$$

Commented by cortano1 last updated on 22/Jan/22

$$bycalculator$$

Commented by cortano1 last updated on 22/Jan/22

����������

Answered by MJS_new last updated on 22/Jan/22

$${\log }_{12}3=a\iff {\log }_{5}2=b$$$$\mathrm{or}\mathrm{else}\mathrm{solve}\mathrm{this}:\sqrt[17]{29}=\alpha ,\sqrt[13]{7}=?$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com