Given that log y=log(10x^n).make n the subject of the formula
just recall that exponents and logs are inverse operations, like + and - or * and /.
y = log(10x^n)
10^y = 10x^n
x^n = 10^y/10 = 10^(y-1)
x = 10(y-1)/n
To solve for n in the equation log y = log(10x^n), we can use the fact that if the logarithms have the same base, then the arguments must be equal. In this case, since both logarithms have base 10, we can equate the arguments:
10x^n = y
Next, we can divide both sides of the equation by 10:
x^n = y/10
To isolate n, we need to get rid of the exponent n. We can do this by taking the logarithm of both sides of the equation with base x:
logx(x^n) = logx(y/10)
Using the logarithmic identity logb(b^c) = c, we can simplify the left side:
n = logx(y/10)
Hence, n is the natural logarithm of y divided by 10 with base x.
However, it's important to note that the answer depends on the logarithm's base (x) and the value of y. Without specific values for these variables, it is not possible to provide an exact expression for n.