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

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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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chrisbond437 | Student, Grade 10 | (Level 1) Honors

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Considering 6^x +6^x +6^x +6^x +6^x 6^x =11,

6^2x+4*6^x-11=0.

this is a quadratic equation in 6^x. but it will have imaginary roots so this will not be posssible.

if it is 6^x +6^x +6^x +6^x +6^x +6^x=11

6^(x+1)=11

6^(x+1)=6+5

6.6^x-6=5

6[(6^x)-1]=5

6^x-1=5/6

6^x=11/6

6^x=1.83333...

thus x=logarithm of 11/6 to the base 6

x=0.33829082295831 [using online log calculator]

http://www.ajdesigner.com/phplogarithm/log_equation_base_any_y.php

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