How do you expand ${log}_{b} (\frac{\sqrt{57}}{74})$ $Log_b( sqrt57/74)$ ?

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Answer 1 · 2016-05-20T02:38:43

$\frac{(\frac{1}{2}) log 57 - log 74}{log b} = \frac{(\frac{1}{2}) ln 57 - ln 74}{ln b}$ $((1/2) log 57 - log 74)/log b=((1/2) ln 57 - ln 74)/ln b$

Use ${log}_{b} a = \frac{{log}_{c} a}{{log}_{c} b} and {log}_{b} a^{n} = n {log}_{b} a$ $log_b a=log_c a/log_c b and log_b a^n=n log_b a$ .

Here, the given logarithm

$= {log}_{b} (\frac{\sqrt{57}}{74})$ $= log_b( sqrt57 /74)$

$= \frac{log (\frac{\sqrt{57}}{74})}{log b} = \frac{ln (\frac{\sqrt{57}}{74})}{ln b}$ $=log( sqrt57 /74)/log b=ln( sqrt57 /74)/ln b$

$= \frac{\frac{log 57}{2} - log 74}{log b} = \frac{\frac{ln 57}{2} - ln 74}{ln b}$ $=( log 57/2 - log 74)/log b=( ln 57/2 - ln 74)/ln b$

How do you expand logb(√5774)Log_b( sqrt57/74)?