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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


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!!!


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.


Mark M.

Use of change of base is permissible, yet not necessary, viz., my solution. 


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