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Question Number 166619 by BagusSetyoWibowo last updated on 23/Feb/22

$$\frac{2}{{\log }_{10}\left(6\right)}=\frac{{\pi }^x}{7}$$$$Howmuchthexis?$$

Answered by TheSupreme last updated on 23/Feb/22

$$\frac{{log}_{10}\left(100\right)}{{log}_0\left(6\right)}={log}_6\left(100\right)=\frac{{\pi }^x}{7}$$$${\pi }^x=7{log}_6\left(100\right)$$$$x={log}_{\pi }\left(7{log}_6\left(100\right)\right)$$

Commented by BagusSetyoWibowo last updated on 24/Feb/22

$$AnotherMethod$$$$\frac{2}{{\log }_{10}\left(6\right)}=\frac{{\pi }^x}{7}$$$$Crossmultiplyif\frac{a}{b}=\frac{c}{d}$$$$a\times d=b\times c$$$$2\times 7={\log }_{10}\left(6\right)\times {\pi }^x$$$$14={\log }_{10}\left(6\right)\times {\pi }^x$$$$Dividebothsidesby{\log }_{10}\left(6\right)$$$$\frac{14}{{\log }_{10}\left(6\right)}=\frac{{\log }_{10}\left(6\right){\pi }^x}{{\log }_{10}\left(6\right)}$$$$Switchsides$$$${\pi }^x=\frac{14}{{\log }_{10}\left(6\right)}$$$$Applyexponentrule$$$$x\ln \left(\pi \right)=\ln \left(\frac{14}{{\log }_{10}\left(6\right)}\right)$$$$Solve$$$$x=\frac{\ln \left(\frac{14}{{\log }_{10}\left(6\right)}\right)}{\ln \left(\pi \right)}$$$$x=2,524518...$$$$$$

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