3x5logx4 fx find least integerSolutionAnswer 3x5 logx4 Now

3x^5+(logx)^4 = f(x) find least integer

Answer:

3x^5 + (logx)^4

Now , 3x^5 + (logx)^4 < = x^n

=> 3x^5 + (logx)^4 = x^n

taking log on both sides , we get

log [ 3x^5 + (logx)^4 ] = logx^n

=> log [ 3x^5 + 4logx ] = logx^n

log ( 3x^5 * logx) = logx^n

3x^5 * logx = logx^n

3x^5 * x = x^n

3 log(x^5 *x) = nlogx

3log(x^5*x) = nlogx

3log(x^6) = nlogx

18logx= nlogx => n = 18

Therefore n = 18.