express log (base b) 2 +log (base b) beta + (1/2)log (base b)Y- (1/2)log(base b) w as a single logarithm? (P.S: I think that w is an angular speed symbol) Thank you!! sooo much for reading and repling!!
Remember, the sum of logarithms with the same base is the same as the logarithm of all those things inside multiplied together. That is:\[\log_{a}(x)+\log_{a}(y)+\log_{a}(z)...\log_{a}(n)=\log_{a}(x \times y \times z ...\times n) \]We also know that if the logarithms were being subtracted instead of being added, then instead of multiplying, we would divide them. And we also know that the exponent of a logarithm can be brought over to the front and be multiplied by the whole thing. From this we can re-write your given logarithm as: \[\log_{b}(2) +\log_{b}(\beta) +\frac{ 1 }{ 2 }\log_{b}(Y)-\frac{ 1 }{ 2 }\log_{b}w=\log_{b}(2 \times \beta \times Y^{1/2} )-\log_{b} w^{1/2}\]\[=\log_{b}\left( \frac{ 2 \times \beta \times Y^{1/2} }{ w^{1/2} } \right) =\log_{b}\left( \frac{ 2 \beta \sqrt{ Y} }{ \sqrt{w} } \right)\] @Tayseer
Yes! I understand now! Thank You sooo much! You are the best
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