step 1 So in the given question we have an equation an exponential equation that is given as 9 raised t

(9^3-5 x)(7^5 x-3)=1

Name: Problem 102, Chapter 7: Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry
Uploaded: 2021-07-29T16:47:44-08:00
Duration: 1 min 40 s
Channel: Anas Venkitta
Description: (9^3-5 x)(7^5 x-3)=1

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Key Concepts

Substitution Technique

The substitution technique involves introducing a new variable to replace a recurring or complex expression, thereby reducing the equation to a more manageable form. This approach is particularly useful in exponential equations where the same linear combination of variables appears in multiple exponents.

Exponential Equations

Exponential equations are equations where the variable appears in the exponent. They require techniques that leverage the properties of exponential and logarithmic functions, such as rewriting expressions with a common base or applying logarithms to both sides of the equation, to isolate and solve for the variable.

Properties of Exponents

The properties of exponents, such as the rule that any nonzero number raised to the power of zero equals one and the ability to combine or split exponents when bases are multiplied, are essential for simplifying and solving exponential expressions. Recognizing how to manipulate these properties allows one to transform complex exponential expressions into simpler forms.

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