log(2) = X
can be expressed exponentially like this, because by the definition of logs( base 10) this is what this means.
10^X = 2
take natural log each side
ln(10^X) = ln(2)
you have right to place X in front of ln
X ln(10) = ln(2)
X = ln(2)/ln(10) ( not ln(2/10)!! )
X = 0.3010299957
check
10^0.3010299957
= 2
checks
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I guess you mean log2{log2[log2(x)]} = 0 ?Let Y = {log2[log2(x)]}, so you have log2[Y] = 0The solution to this is Y = 1,Then you a simpler equation: log2[log2(x)] = 1Let Z = log2(x), so log2[Z] = 1, solves to Z = 2,so log2(x) = 2, and x = 4
[log2 (x - 3)](log2 5) = 2log2 10 log2 (x - 3) = 2log2 10/log2 5 log2 (x - 3) = 2(log 10/log 2)/(log5/log 2) log2 (x - 3) = 2(log 10/log 5) log2 (x - 3) = 2(1/log 5) log2 (x - 3) = 2/log 5 x - 3 = 22/log x = 3 + 22/log 5
Find 102a if log2=a and log3=b B has no purpose in this question If a=log2, then 102a =102(log2)
log2(31000) = 1000 log2(3)log2(3) = 1.585 (rounded)1000 log2(3) = log2(31000) = 1,584.96(rounded)
To solve the equation 3log5 125 - log2 8 = x, you can use the properties of logarithms. First, simplify the logarithmic expressions: 3log5 125 simplifies to log5 (125^3), and log2 8 simplifies to log2 (2^3). This gives you log5 15625 - log2 8 = x. Then, you can combine the logarithms using the quotient rule to get log5 (15625/8) = x. Finally, simplify the expression inside the logarithm to get x = log5 1953.125.