Log base 4 64 without using a calculator

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To find log base 4 of 64 without a calculator, recognize that it represents the exponent x in the equation 4^x = 64. The solution can be derived by rewriting 64 as 4 raised to the power of 3, since 4^3 equals 64. Thus, log_4(64) simplifies to 3, as log_4(4^3) equals 3 times log_4(4), which is 1. This method clarifies the calculation and boosts understanding of logarithmic functions. The discussion concludes with a positive acknowledgment of grasping the concept.
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i don't understand how to find the exact answer to log base 4 64 without using a calculator. can anyone help?my teacher gave examples but they are on bad photocopies
sarah
 
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log_4(64) is the number x such that 4^x = 64. Have you tried to guess the solution?
 
Hes right.
log_4 64 = log_4 4^3 = 3log_4 4 = 3(1) = 3
 
thanks guys i totally get itnow and idont feel too stuupid anymore!
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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