Question and Answers Forum

All Questions      Topic List

Arithmetic Questions

Previous in All Question      Next in All Question      

Previous in Arithmetic      Next in Arithmetic      

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

(4.2)^x =100

$$\left(\mathrm{4}.\mathrm{2}\right)^{{x}} =\mathrm{100} \\ $$$$ \\ $$$$ \\ $$

Answered by alephzero last updated on 08/Feb/22

(4.2)^x = 100 ⇒ (((21)/5))^x = 100 ⇒ log_((21)/5) (((21)/5))^x = log_((21)/5) 100 ⇒ x = log_((21)/5) 100 ⇒ x = 2 log_(4.5) 100 ≈ 3.2

$$\left(\mathrm{4}.\mathrm{2}\right)^{{x}} \:=\:\mathrm{100} \\ $$$$\Rightarrow\:\left(\frac{\mathrm{21}}{\mathrm{5}}\right)^{{x}} \:=\:\mathrm{100} \\ $$$$\Rightarrow\:\mathrm{log}_{\frac{\mathrm{21}}{\mathrm{5}}} \left(\frac{\mathrm{21}}{\mathrm{5}}\right)^{{x}} \:=\:\mathrm{log}_{\frac{\mathrm{21}}{\mathrm{5}}} \mathrm{100} \\ $$$$\Rightarrow\:{x}\:=\:\mathrm{log}_{\frac{\mathrm{21}}{\mathrm{5}}} \mathrm{100} \\ $$$$\Rightarrow\:{x}\:=\:\mathrm{2}\:\mathrm{log}_{\mathrm{4}.\mathrm{5}} \mathrm{100}\:\approx\:\mathrm{3}.\mathrm{2}\:\:\: \\ $$

Answered by MJS_new last updated on 09/Feb/22

(((21)/5))^x =100 xln ((21)/5)=ln 100 x=((ln 100)/(ln ((21)/5)))=((2(ln 5 +ln 2))/(ln 7 −ln 5 +ln 3))≈3.20898881204

$$\left(\frac{\mathrm{21}}{\mathrm{5}}\right)^{{x}} =\mathrm{100} \\ $$$${x}\mathrm{ln}\:\frac{\mathrm{21}}{\mathrm{5}}=\mathrm{ln}\:\mathrm{100} \\ $$$${x}=\frac{\mathrm{ln}\:\mathrm{100}}{\mathrm{ln}\:\frac{\mathrm{21}}{\mathrm{5}}}=\frac{\mathrm{2}\left(\mathrm{ln}\:\mathrm{5}\:+\mathrm{ln}\:\mathrm{2}\right)}{\mathrm{ln}\:\mathrm{7}\:−\mathrm{ln}\:\mathrm{5}\:+\mathrm{ln}\:\mathrm{3}}\approx\mathrm{3}.\mathrm{20898881204} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com