Question

Find the value of m if
3m x 3raise to the power of 10= 3 raise to the power of 5
​

Answer 1

Step-by-step explanation:

Given:-

$\sf 3^m\times 3^{10}=3^5$

To find:-

Value of m

Solution:-

$\\\qquad\qquad\displaystyle\sf {:}\rightarrowtail 3^m\times 3^{10}=3^5$

$\\\qquad\qquad\displaystyle\sf {:}\rightarrowtail 3^{m+10}=3^5$

$\\\qquad\qquad\displaystyle\sf {:}\rightarrowtail m+10=5$

$\\\qquad\qquad\displaystyle\sf {:}\rightarrowtail m=5-10$

$\\\qquad\qquad\displaystyle\sf {:}\rightarrowtail m=-5$

$\therefore\st m=-5$

More to know:-

$\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}$