log(a)10+13log(a) x=log(a)30

Question

Could you please explain how you got the answer, please?

Answer 1

logxy= logx +logy is a general formula for logs of any base as long as the base is the same

also, blogx = log(x^b) such as 13log(a)x = log(a)(x^13) You can change the coefficient to a power

log(a)10 +13log(a)(x) = log(a)30

log(a)10+ log(a)(x^13) = log(a)30

log(a)(10x^13) = log(a)30

a^log(a)(10x^13) = a^log(a)30

10x^13 = 30

x^13 = 3

x = the 13th root of 3 = 1.08818... = about 1.09 (1.09^13) = about 3

x= about 1.09