How do you solve 12=10^(x+5)-7?

1 Answer
Sep 10, 2016

x = log_(10)(19) - 5

Explanation:

We have: 12 = 10^(x + 5) - 7

Let's add 7 to both sides of the equation:

=> 19 = 10^(x + 5)

=> 10^(x + 5) = 19

Then, let's apply log_(10) to both sides of the equation:

=> log_(10)(10^(x + 5)) = log_(10)(19)

Using the laws of logarithms:

=> (x + 5) log_(10)(10) = log_(10)(19)

=> (x + 5) cdot 1 = log_(10)(19)

=> x + 5 = log_(10)(19)

Now, to solve for x, let's subtract 5 from both sides:

=> x = log_(10)(19) - 5