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# solve for x : log base 9 X^2=9

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solve for x : log base 9 X^2=9

Guest Aug 6, 2015

#2
+20711
+10

$$\small\text{ Solve for x : \log_9{(x^2)}=9 }}$$

$$\small{\text{Formula: \boxed{~ \log_b{(b^a)}=a~}}}\\\\ \small{\text{ We have b=9, and a = 9 so \log_9{(9^9)}=9, but 9^9 is x^2 }}\\\\ \small{\text{ \begin{array}{rcl} x^2 &=& 9^9\\ x &=& 9^{\frac{9}{2}}\\ x &=& \left(\sqrt{9} \right)^9\\ x &=& \left(\sqrt{3^2} \right)^9\\ x &=& 3^9\\ \mathbf{x} & \mathbf{=} & \mathbf{19683}\\ \\ \hline \\ \end{array} }}\\$$

heureka  Aug 6, 2015
#1
+94202
+10

$$\\log_9x^2=9\\\\ 2log_9x=9\\\\ log_9x=9/2\\\\ 9^{log_9x}=9^{9/2}\\\\ x=9^{9/2}\\\\ x=3^9\\\\ x=19683$$

check:

$${{log}}_{{\mathtt{9}}}{\left({{\mathtt{19\,683}}}^{{\mathtt{2}}}\right)} = {\mathtt{9}}$$

Melody  Aug 6, 2015
#2
+20711
+10

$$\small\text{ Solve for x : \log_9{(x^2)}=9 }}$$

$$\small{\text{Formula: \boxed{~ \log_b{(b^a)}=a~}}}\\\\ \small{\text{ We have b=9, and a = 9 so \log_9{(9^9)}=9, but 9^9 is x^2 }}\\\\ \small{\text{ \begin{array}{rcl} x^2 &=& 9^9\\ x &=& 9^{\frac{9}{2}}\\ x &=& \left(\sqrt{9} \right)^9\\ x &=& \left(\sqrt{3^2} \right)^9\\ x &=& 3^9\\ \mathbf{x} & \mathbf{=} & \mathbf{19683}\\ \\ \hline \\ \end{array} }}\\$$

heureka  Aug 6, 2015