How to solve for x

Question

6^x=0.25^2x-1

 

x/2x-1=log(0.25)/log(6) 

 

I've got so far.

Answer 1

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.

Answer 2

Alain,

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!