find the value of x pleaes find the value of x for which: 6^x +6^x +6^x +6^x +6^x 6^x =11

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Notice that there are 6 terms of 6^x, therefore you may write the simplified equation such that:

6*6^x = 11

Use the property of exponentials: 6*6^x = 6^(1+x)

Write the equation: 6^(1+x) = 11

Using logarithmation yields:

ln(6^(1+x)) = ln11 => (1+x)ln6 = ln11

ln 6 + xln6 = ln11

Subtracting ln 6 both sides yields: xln6 = ln 11 - ln 6

xln6 = ln(11/6) => x =  ln(11/6)/ln 6

The solution to the given exponential equation is x =  ln(11/6)/ln 6.

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