How do you solve #10^(x-1)=100^(2x-3)#?

1 Answer
Jun 18, 2018

#x=5/3#

Explanation:

Let's rewrite the right side in terms of base-#10#. This gives us

#10^(x-1)=color(blue)(10^((2)*(2x-3))#

Notice, #10^2=100#, so we didn't change the value of the equation.

#=>10^(x-1)=10^(4x-6)#

Since we have the same bases, the exponents are equivalent. We can now set up the following equation:

#x-1=4x-6#

Subtracting #4x# from both sides gives us

#-3x-1=-6#

Adding #1# to both sides, we get

#-3x=-5#

Lastly, dividing both sides by #-3#, we get

#x=5/3#

Hope this helps!