Question

find the value of x : (3/5)^x (5/3)2x = 125/27

Answer 1

(3/5)^x * (5/3)^2x. = 125/27

So,

(5/3)^{-x} * (5/3)^2x =125/27

Further simplifying the expression

(5/3)^x =125/27

(5/3)^x =(5/3)^3

So from here clearly x = 3

Answer 2

Concept:

Exponents and power:

1) When the expressions having same base are multiplied, the powers are added. For example, a⁷ × a³ = a⁷⁺³ = a¹⁰

2) Negative exponent. 1/a⁸ = a⁻⁸

Given:

(3/5)^x (5/3)^2x = 125/27

(3/5)ˣ (5/3)²ˣ = 125/27

Find:

The value of x.

Answer:

The value of x is 3.

Solution:

The given expression is,

(3/5)ˣ (5/3)²ˣ = 125/27

Now, for solving, first, we need to make the bases the same on the left-hand side. For this, we will reciprocate the first base.

[1/(3/5)]⁻ˣ [5/3]²ˣ = 125/27

On reciprocating, power becomes negative.

∴ (5/3)⁻ˣ (5/3)²ˣ = 125/27

Now, the base is same and the expressions are in multiplication, according to rule 1) mentioned above, we get

$(5/3)^{2x + (-x)} = 125/27\\(5/3)^{2x - x} = 125/27\\(5/3)^x = 125/27\\(5/3)^x = (5\times 5\times 5)/3\times 3\times 3)\\(5/3)^x = (5/3)^3$

On equating, we get

x = 3

Hence, the value of x is 3.

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