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 181154 by mathlove last updated on 22/Nov/22

$${\left({log}_{15}5\right)}^2+\left({log}_{15}3\right)\left({log}_{15}75\right)=?$$$$$$

Answered by SEKRET last updated on 22/Nov/22

$${\mathbf{log}}_{15}\left(3\right)=\mathbf{a}{\mathbf{log}}_{15}^{}\left(5\right)=1-\mathbf{a}$$$${\mathbf{log}}_{15}(15\cdot 5)=1+{\mathbf{log}}_{15}\left(5\right)=2-\mathbf{a}$$$${(1-\mathbf{a})}^2+\mathbf{a}\cdot (2-\mathbf{a})={\mathbf{a}}^2-2\mathbf{a}+1+2\mathbf{a}-{\mathbf{a}}^2=1$$$$\mathbf{answer}1$$$$\mathit{A}\mathit{B}\mathit{D}\mathit{U}\mathit{L}\mathit{A}\mathit{Z}\mathit{I}\mathit{Z}\mathit{A}\mathit{B}\mathit{D}\mathit{U}\mathit{V}\mathit{A}\mathit{L}\mathit{I}\mathit{Y}\mathit{E}\mathit{V}$$

Commented by mathlove last updated on 22/Nov/22

$$thanks$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com