If 2250 = 2a. 3b. 5c, Find A, B and C. Hence, Calculate the Value of 3a X 2-b X 5-c. - Mathematics

If 2250 = 2^a. 3^b. 5^c, find a, b and c. Hence, calculate the value of 3^a x 2^-b x 5^-c.

Sum

Given 2250 = 2^a · 3^b · 5^c
⇒ 3² x 5³ x 2 = 2^a · 3^b · 5
⇒ a = 1, b = 2, c = 3
3^a x 2^-bx 5^-x
= 3¹ x 2^-2x 5^-3

= `(3)/(2^2 xx 5^3)`

= `(3)/(500)`.

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Solving Exponential Equations

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Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 19

Solve for x : 2^2x+1 = 8

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`("a"^"m"/"a"^"n")^("m"+"n"+1) ·("a"^"n"/"a"^1)^("n" + 1-"m").("a"^1/"a"^"m")^(1+"m"-"n")`

Prove the following:

`root("ab")(x^"a"/x^"b")·root("bc")(x^"b"/x^"c")·root("ca")(x^"c"/x^"a")` = 1