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Solve for x: log_x ⁡16 = 1/2 - Mathematics

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Question

Solve for x:

`log_x 16 = 1/2`

Sum
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Solution

Given: `log_x 16 = 1/2`

Step-wise calculation:

1. Convert to exponential form:

`x^(1/2) = 16`

2. Square both sides to solve for x:

x = 162

x = 256

3. Check base conditions for a logarithm:

Base x must be positive and not 1. 

x = 256 satisfies these.

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Chapter 7: Logarithms - Exercise 7A [Page 140]

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Nootan Mathematics [English] Class 9 ICSE
Chapter 7 Logarithms
Exercise 7A | Q 6. (v) | Page 140
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