solve x^(log base3 x) =9
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solve x^(log base3 x) =9
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Verified answer
☺Question:-
solve x^(log base3 x) =9
☺Solution:-
Given:-
9x = log - 3x=log
9 x+log 3 x= 23
☞Using base change property of log:-
log ab=log , b log a
ab= loga , logb
log xlog 9+log × log = 32
log9logx + log3 logx = 23☺
☞using property of exponent:-
log a^m=mlog alogam =mloga
log x 2 log 3+ log x log 3 =23
2log3 logx + log3 logx = 23☺
☞make same denominator:-
log x+2log x2log 3=33
2log3
logx+2logx = 23
using addition property of log
log a+log b = log abloga+logb= logab☺
log x log 3=32
2log3
logx 3 = 23log x^3log 3^3logx
3 =log3☺
☞Answer:-
x^3=3^3x 3=3 3 x=3x=3☺
☞Therefore:-
Hence, the value of x is 3
☞Good question !
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