Simplify-log-2-5-log-25-20-log-4-50-log-4-70-log-15-49-

Question Number 24069 by Joel577 last updated on 12/Nov/17

Simplify

\frac{(\log_{2} \sqrt{5} . \log_{25} 20) + \log_{4} \sqrt{50}}{\log_{4} 70 - \log_{15} 49}

Answered by $@ty@m last updated on 12/Nov/17

= \frac{\frac{\log \sqrt{5}}{\log 2} \times \frac{\log 20}{\log 25} + \frac{\log \sqrt{50}}{\log 4}}{\frac{\log 70}{\log 4} - \frac{\log 49}{\log 15}}

= \frac{\frac{\log 5}{2 \log 2} \times \frac{(\log 2 + \log 10)}{2 \log 5} + \frac{(\log 5 + \log 10)}{4 \log 2}}{\frac{(\log 7 + \log 10)}{2 \log 2} - \frac{2 \log 7}{\log 15}}

= \frac{\frac{(\log 2 + 1)}{4 \log 2} + \frac{(\log 5 + 1)}{4 \log 2}}{\frac{\log 15 (\log 7 + 1) - 4 \log 7 . \log 2}{2 \log 2 . \log 15}}

= \frac{\frac{(\log 2 + \log 5 + 1)}{4 \log 2}}{\frac{\log 15 (\log 7 + 1) - 4 \log 7 . \log 2}{2 \log 2 . \log 15}}

= \frac{\frac{2}{4 \log 2}}{\frac{\log 15 (\log 7 + 1) - 4 \log 7 . \log 2}{2 \log 2 . \log 15}}

= \frac{\frac{1}{2 \log 2}}{\frac{\log 15 (\log 7 + 1) - 4 \log 7 . \log 2}{2 \log 2 . \log 15}}

= \frac{\log 15}{\log 15 (\log 7 + 1) - 4 \log 7 . \log 2}

Commented by math solver last updated on 12/Nov/17

does this means simplification {just

asking} coz

as i was trying i could not get a single

answer so thought i would be wrong

somewhere .

Commented by $@ty@m last updated on 12/Nov/17

N o m o r e s i m p l i f i c a t i o n p o s s i b l e .

A t t h e m o s t y o u c a n f i n d i t s n u m e r i c a l

v a l u e u s i n g l o g t a b l e o r s c i . c a c u l a t o r

Commented by $@ty@m last updated on 12/Nov/17

Commented by Joel577 last updated on 13/Nov/17

Y e s, I a l s o t h o u g h t t h e r e w a s s o m e t h i n g

w r o n g w i t h t h i s q u e s t i o n

Commented by Joel577 last updated on 13/Nov/17

B t w, t h a n k y o u v e r y m u c h

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