Question

given log5=.6990 find the value of log2 and log2.5​

Answer 1

$log(5) = 0.6990 \\ log(10) = 1 \\ \\ as \: log(xy) = log(x) + log(y) \\ \\ log(10) = log(5 \times 2) = log(5) + log(2) \\ 1 = 0.6990 + log(2) \\ 1 - 0.6990 = log(2) \\ 0.3010 = log(2)$

$log(5) = 0.6990 \\ log(2) = 0.3010 \: \: \: \: (stated \: above) \\ \\ as \: log(xy) = log(x) + log(y) \\ log(5) = log(2.5 \times 2) = log(2.5) + log(2) \\ 0.6990 = log(2.5) + 0.3010 \\ 0.6990 - 0.3010 = log(2.5) \\ 0.3980 = log(2.5)$

this is the method used here

formula used:

log(xy)= log(x)+log(y)

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