Question
Find the value of: $\log _{\sqrt{3}}(3 \sqrt{3})$
✓
Answer
$\log _{\sqrt{3}}(3 \sqrt{3}) $
Let $\log _{\sqrt{3}}(3 \sqrt{3})= x$
$ \Rightarrow(\sqrt{3})^x=3 \sqrt{3}$
$ \Rightarrow 3^{\frac{x}{2}}=3^{1+\frac{1}{2}}=3^{\frac{3}{2}} $
$ \therefore \frac{x}{2}=\frac{3}{2} $
$ \Rightarrow x =3 .$
Let $\log _{\sqrt{3}}(3 \sqrt{3})= x$
$ \Rightarrow(\sqrt{3})^x=3 \sqrt{3}$
$ \Rightarrow 3^{\frac{x}{2}}=3^{1+\frac{1}{2}}=3^{\frac{3}{2}} $
$ \therefore \frac{x}{2}=\frac{3}{2} $
$ \Rightarrow x =3 .$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Express $\frac{13}{34}$ as a decimal, correct to three decimal places.
→Prove that the angle subtended at the centre of a circle, is bisected by the radius passing through the mid-point of the arc.
If $(a+b)=2$ and $(a-b)=10$, find the values of : $a b$.
→Solve for $x :p ^{-5}=\frac{1}{ p ^{x+1}}$
→The points A(3, 2) B(0, 5) and D(0, - 1) are the three vertices of a square ABCD. Plot these points on a graph paper and hence find the co-ordinates of the vertex C.
$AD$ and $BE$ are altitudes of an isosceles $\triangle ABC$ with $AC = BC.$ Prove that $AE = BD.$
→ In a triangle $ABC.$ If $D$ is a point on $BC$ such that $\angle CAD = \angle B,$ then prove that$: \angle ADC = \angle BAC.$
→Construct a parallelogram $\text{ABCD},$ when$:AB = 4.4 \ cm, AD = 6.2 \ cm$ and $AC = 4.8 \ cm.$
→If $\frac{3}{2} \log a+\frac{2}{3} \log b-1=0$, find the value of $a^9 \cdot b^4$.
→Construct a parallelogram PQRS in which $QR =4.7 cm, \angle Q =120^{\circ}$ and $PQ =2.8 cm$.
→