Question

logx 32=10/3 find x​

Answer 1

Answer:

logx=1/x

1/x×32=10/3

32/x=10/3

10x=96

x=96/10

x=9.6

Answer 2

The value of $x=2\sqrt{2}$

Step-by-step explanation:

We have,

$\log_x 32=\dfrac{10}{3}$

To find, the value of x = ?

∴ $\log_x 32=\dfrac{10}{3}$

⇒ $\log_x 2^5=\dfrac{10}{3}$

[ ∵ 32 = 2 × 2 × 2 × 2 × 2]

⇒ $5\log_x 2=\dfrac{10}{3}$

[ ∵ $\log a^m= m\log a$]

⇒ $\log_x 2=\dfrac{10}{3\times 5}$

⇒ $\log_x 2=\dfrac{2}{3}$

By property of logarithm,  

⇒ $x^{\frac{2}{3}}=2$

⇒ $x=2^{\dfrac{3}{2}}$

⇒ $x=2\sqrt{2}$

Hence, the value of $x=2\sqrt{2}$