How do you solve #10^(x-3)=100^(4x-5)#?

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Answer 1 · 2016-09-21T21:31:35

#x = 1#

We have: #10^(x - 3) = 100^(4 x - 5)#

Let's express both sides of the equation in terms of #10#:

#=> 10^(x - 3) = (10^(2))^(4 x - 5)#

Using the laws of exponents:

#=> 10^(x - 3) = 10^(8 x - 10)#

#=> x - 3 = 8 x - 10#

#=> 7 x = 7#

#=> x = 1#

Therefore, the solution to the equation is #x = 1#.