Question

If 15^27÷15^2 =15^-2×15^5m+2 find the value of 3m-3×2^3-m

Answer 1

Question :- If 15^27 ÷ 15^2 =15^(-2) × 15^(5m+2) find the value of 3m - 3×2^(3-m) ?

Solution :-

→ 15^27 ÷ 15^2 =15^(-2) × 15^(5m+2)

using in LHS :-

• a^b ÷ a^c = a^( b - c)

using in RHS :-

• a^b * a^c = a^(b + c)

we get :-

→ 15^(27 - 2) = 15^( - 2 + 5m + 2)

→ 15^25 = 15^(5m)

using a^b = a^c => b = c , we get,

→ 5m = 25

Dividing both sides by 5 , we get,

→ m = 5 .

Now, putting value of m , we get,

→ 3m - 3 * 2^(3 - m)

→ 3*5 - 3 * 2^(3 - 5)

→ 15 - 3 * 2^(-2)

using a^(-b) = 1/a^b,

→ 15 - 3 * 1/2²

→ 15 - (3/4)

→ (60 - 3)/4

→ (57/4). (Ans.)

Learn More :-

which expressions are equivalent to 13^6 divided (13^8)(13^-4)/13^-2

https://brainly.in/question/23169677?utm_source=android&utm_medium=share&utm_campaign=question