Alain G.

asked • 12/15/13# How to solve for x

6^x=0.25^2x-1

x/2x-1=log(0.25)/log(6)

I've got so far.

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## 2 Answers By Expert Tutors

Charles D. answered • 12/16/13

Patient and Knowledgeable Tutoring by Charles

Alain,

You were on the right track with the amount of work you did but you just need to finish it. Starting with the following:

x/(2x-1) = Log(0.250/log(6)

Now evaluate and divide the logarithms on the right side and you should get:

x/(2x-1) = -0.7737056145 *I write down the entire value shown on the calculator*

Now multiply both sides by (2x-1) and you should get:

x = -0.7737056145(2x-1)

Using the Distributive Property on the right side you should get:

x = -1.547411229x + 0.7737056145

Now add +1.547411229x to both sides and you should get:

x + 1.547411229x = -0.7737056145

Now add 1x to 1.547411229 on the left side of the equation to get:

2.547411229x = -0.7737056145

Now divide both sides by 2.547411229 and you should get:

x = -0.3037223067 which is the value of x.

Like I said, you were on the right track, you just needed to evaluate the logarithms and work with their values for a little while.

William S. answered • 12/15/13

Experienced scientist, mathematician and instructor - William

Am I supposed to interpret this as

6

^{x}= 0.25

^{2x}- 1

or

6

^{x}= 0.25

^{(2x-1)}

It makes a big difference!

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William S.

^{x}= 0.25^{x}- 1^{x}= 0.25^{(x-1)}12/15/13