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Question Number 92488 by hmamarques1994@gmail.com last updated on 07/May/20

$${\left(3\mathrm{x}\right)}^{{\log }_{\mathrm{b}}3}={\left(5\mathrm{x}\right)}^{{\log }_{\mathrm{b}}5}$$$$$$$$\mathrm{x}=?$$

Commented by jagoll last updated on 07/May/20

$${\left(3\right)}^{\log {}_{\mathrm{b}}\left(3\mathrm{x}\right)}={\left(5\right)}^{\log {}_{\mathrm{b}}\left(5\mathrm{x}\right)}$$$$\log {}_{\left(5\mathrm{x}\right)}\left(3\mathrm{x}\right)=\log {}_3\left(5\right)$$$$\log {}_3\left(\mathrm{x}\right)\{1-\log {}_3\left(5\right)\}=(\log {}_3\left(5\right)-1)(\log {}_3\left(5\right)+1)$$$$\log {}_3\left(\mathrm{x}\right)=-\log {}_3\left(15\right)$$$$\Rightarrow \mathrm{x}=\frac{1}{15}$$

Commented by jagoll last updated on 07/May/20

cool man ������

Commented by hmamarques1994@gmail.com last updated on 07/May/20

$$\mathrm{Mito}!:)$$

Commented by john santu last updated on 07/May/20

joos ������

Commented by Ar Brandon last updated on 07/May/20

Which laws of logarithm did you apply, please ? ��

Commented by john santu last updated on 07/May/20

$${\mathrm{a}}^{\log {}_{\mathrm{b}}\left(\mathrm{c}\right)}={\mathrm{c}}^{\log {}_{\mathrm{b}}\left(\mathrm{a}\right)}$$

Commented by Ar Brandon last updated on 07/May/20

�� really ? thanks

Commented by john santu last updated on 07/May/20

$$\log {}_{\mathrm{b}}\left(3\mathrm{x}\right)\log {}_{\mathrm{b}}\left(3\right)=\log {}_{\mathrm{b}}\left(5\mathrm{x}\right)\log {}_{\mathrm{b}}\left(5\right)$$$$\frac{\log {}_{\mathrm{b}}\left(3\mathrm{x}\right)}{\log {}_{\mathrm{b}}\left(5\mathrm{x}\right)}=\frac{\log {}_{\mathrm{b}}\left(5\right)}{\log {}_{\mathrm{b}}\left(3\right)}$$$$\frac{1+\log {}_3\left(\mathrm{x}\right)}{\log {}_3\left(5\right)+\log {}_3\left(\mathrm{x}\right)}=\log {}_3\left(5\right)$$$$1+\log {}_3\left(\mathrm{x}\right)={\left(\log {}_3\left(5\right)\right)}^3+\log {}_3\left(5\right)\log {}_3\left(\mathrm{x}\right)$$$$\log {}_3\left(\mathrm{x}\right)\{1-\log {}_3\left(5\right)\}={\left(\log {}_3\left(5\right)\right)}^2-1$$

Commented by john santu last updated on 07/May/20

$$\mathrm{of}\mathrm{course}.\mathrm{you}\mathrm{can}\mathrm{proof}\mathrm{it}$$

Commented by Ar Brandon last updated on 07/May/20

thank you ��

Commented by jagoll last updated on 07/May/20

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