Log base 4 64 without using a calculator

AI Thread Summary
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.
sarahowen
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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!
 

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