Question

15^3/2×15^x/2=15^8.Find value of x​

Answer 1

✧$\huge \mathcal \red {\underline{\underline{A}}}$ $\huge \mathcal \green {\underline{\underline{N}}}$ $\huge \mathcal \pink {\underline{\underline{S}}}$ $\huge \mathcal \blue {\underline{\underline{W}}}$ $\huge \mathcal \orange {\underline{\underline {E}}}$ $\huge \mathcal \purple {\underline{\underline{R}}}$✧

❥︎ Given :

$15 {}^{ \frac{3}{2} } \times {15}^{ \frac{x}{2} } = {15}^{8}$

❥︎ To Find :

The value of x

❥︎ Solution :

⇒ $15 {}^{ \frac{3}{2} } \times {15}^{ \frac{x}{2} } = {15}^{8}$

⇒ $15 ^{\frac{3}{2} + \frac {x} {2}} = 15^{8}$

Put the powers equivalent as the base is same.

⇒ $\frac {3}{2} + \frac {x} {2} = 8$

⇒ $\frac {3 + x}{2} = 8$

⇒ $3 + x = 8 × 2$

⇒ $3 + x = 16$

⇒ $x = 16 - 3$

⇒ $x = 13$

$\implies \textbf {Hence, the value of x is 13.}$

____________________☆

Answer 2

$\bf\huge{\red{Question←:}}$

• $\bf{15}^{\frac{3}{2}}$ × $\bf{15}^{\frac{x}{2}}$ = $\bf{15}^{8}$.

$\bf\huge{\red{To~find←:}}$

• The value of x

$\bf\huge{\red{Answer←:}}$

$\bf{\red{:→}}$ $\bf{15}^{\frac{3}{2}}$ × $\bf{15}^{\frac{x}{2}}$ = $\bf{15}^{8}$.

$\bf{\red{:→}}$ $\bf{15}^{\frac{3}{2}}$ × $\bf\frac{x}{2}$

$\bf{\bold{\red{As~the~base~is~same,}}}$ $\bf{\bold{\red{put~the~powers~equivalent}}}$

$\bf{\red{:→}}$ $\bf\dfrac{3}{2}$ + $\bf\dfrac{x}{2}$ = 8

$\bf{\red{:→}}$ $\bf\dfrac{3+x}{2}$ = 8

$\bf{\red{:→}}$ 3 + x = 8 × 2

$\bf{\red{:→}}$ 3 + x = 16

$\bf{\red{:→}}$ x = 16 - 3

$\bf{\red{:→ x = 13}}$