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

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Answer 1 · 2018-06-18T21:26:25

#x=5/3#

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!