5^(x+2) - 5^x = 1200Solve to 2 decimal places. Any help would be very much appreciated (:

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`5^(x+2)-5^x = 1200`

We can rewrite this as,

`5^x xx 5^2 -5^x = 1200`

We can take `5^x` out as a factor.

`5^x(5^2-1) = 1200`

`5^x(25-1) = 1200`

`5^x xx 24 = 1200`

`5^x = 50`

We can take log of both sides.

`log(5^x) = log(50)`

`x log 5 = log(5 xx 10)`

`x log 5 = log 5 + log 10`

`x log 5 = log 5 + 1`

`log 5 = 0.69897` from log table.

`x xx 0.69897 = 0.69897 + 1`

`x = 1.69897/0.69897`

`x = 2.43`

 

Therefore, x = 2.43

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