Question

Find m
Plz help
Plz give the explanation also along with the answer​

Answer 1

Step-by-step explanation:

all steps understand easily

Answer 2

Question:

Find the value of: $\sf 3^{m-7} \div 81 =1$

Solution:

Firstly, we will convert 81 and 1 in exponential form, such that 3 is the base.

81 = 3⁴ (3⁴ = 3×3×3×3 = 9×9 = 81)

1 = 3⁰ (a⁰ = 1, law of indices)

Therefore, the equation formed is

$\implies \sf {3^{m-7} \div 3^{4} = 3^{0}}$

$\implies \sf {3^{m-7-4} = 3^{0}}$

$\bigstar {\sf {\pink {a^{m} \div a^{n} = a^{m-n}}}}$

$\implies \sf {3^{m-11} = 3^{0}}$

$\bigstar {\sf {\pink {On\ equating\ the\ powers\ of\ 3.}}}$

$\implies \sf {m-11 = 0}$

$\implies \sf {m = 11}$

Verification:

Substitute the value of m as 11 in the equation,

$\implies \sf {3^{m-7} \div 3^{4} = 3^{0}}$

$\implies \sf {3^{11-7} \div 3^{4} = 3^{0}}$

$\implies \sf {3^{4} \div 3^{4} = 3^{0}}$

$\implies \sf {3^{4-4} = 3^{0}}$

$\bigstar {\sf {\pink {a^{m} \div a^{n} = a^{m-n}}}}$

$\implies \sf {3^{0} = 3^{0}}$

$\implies \sf {1 = 1}$

LHS = RHS

Hence Verified!

Value of m:

Value of m is 11.