find x In10^x=loge^x+2

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I'm not sure where to start

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In10^x=loge^x+2
log(base e)10^x =loge^x+2

not sure where to go from there

xln10=xloge+2

I'm really stuck that's as far as I can get

xln10=xloge+2

You're almost there!

If the problem was this: Ax = Bx+2 and you wanted to solve for x how would you do it? Apply the same process here. Remember that ln(10) and log(e) are just numbers, so you can add and subtract them just as you do with numbers in algebra.