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The solution of the equation `(log)_7(log)_5(sqrt(x+5)+sqrt(x)=0`is... |
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Answer» `log_7 (log_5 (sqrt(x+5)+sqrtx))=0` `log_5(sqrt(x+5)+sqrtx))=7^0=1` `sqrt(x+5)+sqrtx=5^1=5` Squaring both sides `x+5+x+2sqrtxsqrt(x+5)=25` `2sqrtxsqrt(x+5)=25-5-2x` `2sqrtxsqrt(x+5)=20-2x=2(10-x)` `sqrtxsqrt(x+5)=10-x` Squaring both sides `x(x+5)=(10-x)^2` `x^2-5x=x^2-20x+100` `25x=100` `x=4` |
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