# log 7 ( 2) + log 7 (x-5) = 2 find x.

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log 7 ( 2) + log 7 (x-5) = 2

We will use algorethim properties to solve:

we know that:

log a b + log a c = log a (b*c)

==> log 7 (2) + log 7 (x-5) = 2

==> log 7 ( 2*(x-5) = 2

==> log 7 ( 2x-10) = 2

Now we will rewrite using the exponent properties:

==> 2x - 10 = 7^2

==> 2x -10 = 49

Now add 10 to both sides:

==> 2x = 59

Now we will divide 2:

==> x= 59/2 = 29.5

**==> x= 29.5**

We have to find x, given that log 7 ( 2) + log 7 (x-5) = 2.

Here we use the relation for logarithms that log(a*b) = log a + log b.

Therefore log 7 ( 2) + log 7 (x-5) = 2

=> log 7 [2*(x-5)] = 2

Now raise 7 to the power of both the sides.

=> 7^[log 7 [2*(x-5)]] = 7^2

=> 2*(x-5) = 7^2

=> 2x -10 = 49

=> 2x = 59

=> x = 59/2

Therefore the solution for x is 59/2.