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Question Number 165799 by pulivendula last updated on 08/Feb/22

$${(4.2)}^x=100$$$$$$$$$$

Answered by alephzero last updated on 08/Feb/22

$${(4.2)}^x=100$$$$\Rightarrow {\left(\frac{21}{5}\right)}^x=100$$$$\Rightarrow {\log }_{\frac{21}{5}}{\left(\frac{21}{5}\right)}^x={\log }_{\frac{21}{5}}100$$$$\Rightarrow x={\log }_{\frac{21}{5}}100$$$$\Rightarrow x=2{\log }_{4.5}100\approx 3.2$$

Answered by MJS_new last updated on 09/Feb/22

$${\left(\frac{21}{5}\right)}^x=100$$$$x\ln \frac{21}{5}=\ln 100$$$$x=\frac{\ln 100}{\ln \frac{21}{5}}=\frac{2(\ln 5+\ln 2)}{\ln 7-\ln 5+\ln 3}\approx 3.20898881204$$

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