How would you solve these simultaneous equations:

y=10^(x)-2 and
y=log10(x+2), x>0

log10, the 10 being the base of the log function

Thank you

One thing to notice is that these 2 equations are actually quite similar. The second one can be re-arranged to give:

x= 10^y - 2.

So from this you can see that x=y.

This then leads you to solve:

x = 10^x - 2

Now this one I don't believe has a closed-form solution. You can get an approximation of the answer using a technique such as Newton's method, or just plug away on your calculator and you can get as many digits of accuracy as you'd like. Hint -the answer is less than 0.5.