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Anthony Y.

asked • 06/10/16

Write answer using base-10 logarithms

Solve for X.
 
2^x-6 = 7^2x
 
Write the exact answer using base-10 logarithms.
 
Help Please.

2 Answers By Expert Tutors

By:

Alexandra W. answered • 06/10/16

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Anthony Y.

I still can't figure it out. Would you be able to give me further help? Thanks!!!
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06/10/16

Alexandra W.

2x(log27) = x - 6 means
2x(log27) - x = -6, so factoring out x we get
x(2log27 - 1) = -6, and so we have
 
x = -6/(2log27 - 1)
 
To put it in terms of base-10 logarithms, you have to use the change of base formula, i.e. logab = log(b)/log(a).
In our case, that means log27 = log7/log2. So
x = -6/(2log27 - 1)
= -6/[(2log7/log2) - 1]
= -6/[(2log7/log2) - (log2/log2)]      (just creating a common denominator here)
= -6/[(2log7 - log2)/log2]
 
= -6log2/(2log7 - log2)
 
That's your final answer. I know this was a complicated problem, so let me know if you have questions on any of the steps, or on logs in general.
 
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06/10/16

Mark M.

Use of change of base is permissible, yet not necessary, viz., my solution. 
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06/10/16

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