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Find X, If : Sqrt( 2^( X + 3 )) = 16 - Mathematics

Sum

Find x, if : `sqrt( 2^( x + 3 )) = 16`

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Solution

`sqrt( 2^( x + 3 )) = 16`

`( 2^( x + 3 ))^(1/2) = 2 xx 2 xx 2 xx 2`

⇒ `( 2 )^[(x + 3)/2] = 2^4`

We know that if bases are equal, the powers are equal.
⇒ `[ x + 3 ]/2 = 4`

⇒ x + 3 = 8
⇒ x = 8 - 3
⇒ x = 5

Concept: Solving Exponential Equations
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 2.2 | Page 100
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