Найдите x, если lg x=2/5 lg 32-1/3 lg 64+1

To solve the equation, we'll simplify the expression on the right side first:

lg x = (2/5) lg 32 - (1/3) lg 64 + 1

Using the properties of logarithms, we can simplify further:

lg x = (2/5) lg (2^5) - (1/3) lg (2^6) + 1 lg x = (2/5) * 5 lg 2 - (1/3) * 6 lg 2 + 1 lg x = 2 lg 2 - 2 lg 2 + 1 lg x = 1

Now we can convert the equation back to exponential form:

x = 10^1 x = 10

Therefore, x is equal to 10.