Menu Close

4-2-x-100-

Tinku Tara 0 Comments
Pin




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

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *