Question

1) 3log3x-2log3x=-22) 2lgx=0,13)lg (x+1)=3

Answer 1

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Answer 2

1) 3log3x - 2log3x = -2

First, we can simplify the left side of the equation using the properties of logarithms.

3log3x - 2log3x = log3(x^3) - log3(x^2)

Using the property loga - logb = log(a/b), we can combine the logarithms.

log3(x^3) - log3(x^2) = log3(x^3 / x^2)

Now, we can simplify x^3 / x^2 to x. So the equation becomes:

log3(x) = -2

To solve for x, we can rewrite the equation in exponential form:

3^(-2) = x

x = 1/9

So the solution to the equation is x = 1/9.

2) 2lgx = 0.1

To solve for x, we can rewrite the equation in exponential form:

10^(0.1) = x

x ≈ 1.2589

So the solution to the equation is x ≈ 1.2589.

3) lg(x+1) = 3

To solve for x, we can rewrite the equation in exponential form:

10^3 = x + 1

x = 1000 - 1

x = 999

So the solution to the equation is x = 999.