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# How to solve for x

6^x=0.25^2x-1

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

I've got so far.

Alain,

Am I supposed to interpret this as

6x = 0.25x - 1

or

6x = 0.25(x-1)

It makes a big difference!
The second one in brackets.
0.25^(x-1)

### 1 Answer by Expert Tutors

Charles D. | Patient and Knowledgeable Tutoring by CharlesPatient and Knowledgeable Tutoring by Ch...
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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.