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Solve for X : (49)X + 4 = 72 X (343)X + 1 - Mathematics

Sum

Solve for x : (49)x + 4 = 72 x (343)x + 1

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Solution

(49)x + 4 = 72 x (343)x + 1

⇒ ( 7 x 7 )x + 4 = 72 ( 7 x 7 x 7 )( x + 1 )

⇒ ( 72 )x + 4  = 72( 73 )( x + 1 )

⇒ 7( 2x + 8 ) = 72 x 73x + 3

⇒ 7( 2x + 8 ) = 73x + 3 + 2

⇒ 7( 2x + 8 ) = 73x + 5
We know that if bases are equal, the powers are equal
⇒ 2x + 8 = 3x + 5
⇒ 3x - 2x = 8 - 5
⇒ x = 3

Concept: Solving Exponential Equations
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 1.4 | Page 100
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