If log27 x=223\text{log}_{\sqrt{27}} \space x = 2\dfrac{2}{3}log27 x=232, find x.
6 Likes
Given,
⇒log27 x=223⇒log27 x=83⇒log33 x=83⇒log332 x=83⇒132 log3 x=83⇒23 log3 x=83⇒ log3 x=83×32⇒ log3 x=4⇒x=34=81.\Rightarrow \text{log}{\sqrt{27}} \space x = 2\dfrac{2}{3} \\[1em] \Rightarrow \text{log}{\sqrt{27}} \space x = \dfrac{8}{3} \\[1em] \Rightarrow \text{log}{\sqrt{3^3}} \space x = \dfrac{8}{3} \\[1em] \Rightarrow \text{log}{3^{\frac{3}{2}}} \space x = \dfrac{8}{3} \\[1em] \Rightarrow \dfrac{1}{\dfrac{3}{2}} \text{ log}{3} \space x = \dfrac{8}{3} \\[1em] \Rightarrow \dfrac{2}{3}\text{ log}{3} \space x = \dfrac{8}{3} \\[1em] \Rightarrow \text{ log}{3} \space x = \dfrac{8}{3} \times \dfrac{3}{2} \\[1em] \Rightarrow \text{ log}{3} \space x = 4 \\[1em] \Rightarrow x = 3^4 = 81.⇒log27 x=232⇒log27 x=38⇒log33 x=38⇒log323 x=38⇒231 log3 x=38⇒32 log3 x=38⇒ log3 x=38×23⇒ log3 x=4⇒x=34=81.
Hence, x = 81.
Answered By
4 Likes
Evaluate :
log3 8 ÷ log9 16
log5 8log 25 16×log 100 10\dfrac{\text{log}5 \space 8}{\text{log }{25} \space 16 \times \text{log }_{100} \space 10}log 25 16×log 100 10log5 8
Show that :
loga m ÷ logab m = 1 + loga b
1loga bc+1+1logb ca+1+1logc ab+1\dfrac{1}{\text{log}{a} \space bc + 1} + \dfrac{1}{\text{log}{b} \space ca + 1} + \dfrac{1}{\text{log}_{c} \space ab + 1}loga bc+11+logb ca+11+logc ab+11
