Question

solve x^(log base3 x) =9​

Answer 1

☺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 !

Keep questioning ☺️.......... .

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