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If `a = log_245 175` and `b = log_1715 875`, then the value of `(1-ab)/(a-b)` is |
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Answer» `175=5xx5xx7` `245=5xx7xx7` `875=5xx5xx5xx7` `1715=5xx7xx7xx7` `a(log_(5)175)/(log_(5)245)=(2+log_(5)7)/(1+2log_(5)7)` `b=(log_(5)875)/(log_(5)1715)=(3+log_(5)7)/(1+3log_(5)7)` Let ` log_(5)y=t` `(1-ab)/(a-b)=(1-((2+t)/(1+2t))((3+t)/(a+3t)))/(((2+t)/(1+2t))-((3+t)/1+3t))` `=(5t^(2)-5)/(t^(2)-1)=5` |
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