logx^3logx^2log14 is 3logx2logxlog14 this equals 6 log14 (logx)^2 So for example, if y=6log14(logx)^2 the log x = square root of (y/6(log14))
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Without tables or calculators, this kinda question is hard, so if there is a non-calculator question involving logs, just chuck numbers in. I find it helpful to rearrange the log into a power problem e.g. log2(x) = 8 --------> x = 28 = 256 or log2(8) = x ----------> 2x = 8 = 3 (by observation) or logx(8) = 2 ----------> x2 = 8, x = (+/-)(root 8) = (+/-)(2root2)
a log is the 'undo-er' of powers, kind of like division is the 'undo-er' of multiplication. EX: 102 = 100, then log10(100) = 2 103 = 1000, then log10(1000) = 3, in this example, we are using log base 10, this is a default base and sometimes isn't even wirten. e is probably the most common base but log base e is more simply called the natural log, or ln. so in general: logx(m) = N means that xN = m so log5(125) = 3 because 53 = 125.
You will need 14 two's multiplied together to equal 16384. the answer to this can be found by log2(16384) = 14. Since most calculators don't have log base 2, you can do this: log(16384)/log(2) = 14. You can use the 'base 10' log or natural log [ln(16384)/ln(2) = 14]
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log(x) + log(2) = log(2)Subtract log(2) from each side:log(x) = 0x = 100 = 1