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If 343 superscript x baseline = 49 superscript 4 minus x, what is the value of x?

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anuksha0456

The value of x is 8/5 or 1.6 when 343ˣ = 49⁴ ⁻ ˣ, using the laws of exponents.

Exponents are of the form aˣ, read as "a to the power of x", and signify the product of a multiplied by itself x number of times.

In the question, we are given that 343ˣ = 49⁴ ⁻ ˣ, and are asked to find the value of x.

We try to solve the exponential equation, using the laws of exponents in the following way:

343ˣ = 49⁴ ⁻ ˣ,

or, (7³)ˣ = (7²)⁽⁴ - ˣ⁾ {Since, 343 = 7³ and 49 = 7²}.

or, 7³ˣ = 7⁸ ⁻ ²ˣ {Using the law: [tex](x^{a})^{b} = x^{ab}[/tex]},

or, 3x = 8 - 2x {Using the law: [tex]x^a = x^b \Rightarrow a = b[/tex], when x ≠ 0}.

or, 3x + 2x = 8 - 2x + 2x {Adding 2x to both sides of the equation},

or, 5x = 8 {Simplifying}

or, 5x/5 = 8/5 {Dividing both sides by 5},

or, x = 8/5 or 1.6 {Simplifying}

Therefore, the value of x is 8/5 or 1.6 when 343ˣ = 49⁴ ⁻ ˣ, using the laws of exponents.

Learn more about exponents at

https://brainly.com/question/20392013

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