Question

(3^x)^5=(3^2)^10 solve this problem by using laws of exponent​

Answer 1

Question :

Using laws of indices find the value of x .

It is given that $(3^x)^5=(3^2)^{10}$

Answer:

$\huge\boxed{\boxed{\green{x=4}}}$

Step-by-step explanation:

Laws of indices :

$(a^n)^m=a^{nm}$

This works for any natural number n and m .

$If\:a^n=a^m\\\\Then\:n=m$

Note that a has to be a natural number .

a must not be equal to 1 nor equal to 0 .

Given :

$(3^x)^5=(3^2)^{10}$

Using $(a^n)^m=a^{nm}$ :

$\implies 3^{5x}=3^{20}$

Using the law that $If\:a^n=a^m\\\\Then\:n=m$

$\implies 5x=20$

Dividing both sides by 5 ( to eliminate the co efficient ) :

$\implies x=\frac{20}{5}$

$\implies x=4$

The value of x will be 4 .

Answer 2

(3^x)^5=(3^2)^10,

To find the value of x?

Good question,

Here is your perfect answer!

As we know (a^m)^n = a^mn,

So =) 3^5x = 3^20

By equating,

=) 5x = 20

=) x = 20/5

=) x = 4.