Question 752631
you did nothing wrong.
the correct answer is x = 15/2.


you can use your calculator to confirm.


log3(x) = log10(x) / log10(3)


since log10 is the calculator LOG function, this can be reduced to:


log3(x) = LOG(x) / LOG(3)


your answer is x = 15/2 = 7.5


replace x in the original equation with 7.5 and you will get:


log3(7.5) - log3(7.5-2) = 1
this simplifies to:
log3(7.5) - log3(2.5) = 1


use the conversion factor to make this equation:


log(7.5)/LOG(3) = LOG(2.5)/LOG(3) = 1


use your calculator to get:


1.8340437671 - .8340437671 = 1


this simplifies to 1 = 1.