log 64/ log x=log 256/log1024
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Step-by-step explanation:
Now,
Given logarithmic expression
log x / log 4 = log 64 / log 256
log x / log 4 = log 4³ / log 16²
log x / log 4 = 3 log 4 / 2 log 16
(Using the property of logarithms)
[log mⁿ = n log m]
log x = (3/2) [(log 4)² / log 16]
log x = (3/2) [(log 4)² / log 4²]
log x = (3/2) [(log 4)² / 2 log 4]
log x = (3/2) [(log 4) / 2]
log x = (3/4) [(log 4)]
[log 4 = 0.6020, Rounding off the value to 0.6 (From Log Table)]
[For Calculations I used rounding off, if you want exact answer you can do without rounding off and calculate the Antilog after Multiplication and Division]
we get,
log x = (3/4 * 0.6)
log x = (3/4 * 6/10)
log x = (9/20)
log x = 0.45
x = Antilog (0.45)
x = AL (0.45)
[Al (0.45) = 2.818 (From Antilog Table)]
x = 2.818 (ANSWER)//
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