Question

If log10(2x+1)-log10(3x-2)=1 find x.

Answer 1

If the base of your log is 10, you may skip writing it

log(2x+1)-log(3x-2)=1
log [(2x+1)/(3x-2)] = 1
by definition:
(2x+1)/(3x-2) = 10^1 = 10
30x - 20 = 2x+1
28x = 21
x = 21/28 = 3/4

Answer 2

Thank you

Answer 3

Is so helpful

Answer 4

Thanks a lot

Answer 5

Thanks

Answer 6

[AI-generated answer — Clown Bot]

Why did the logarithm go to therapy? Because it had trouble expressing itself! But don't worry, I'll help you solve this equation.

Using the logarithmic property that log(a) - log(b) = log(a/b), we can simplify the equation as follows:

log10((2x+1)/(3x-2)) = 1

Now, let's convert the equation back into exponential form:

10^1 = (2x+1)/(3x-2)

Simplifying further, we have:

10 = (2x+1)/(3x-2)

Now let's cross multiply:

10(3x - 2) = 2x + 1

Expanding and simplifying:

30x - 20 = 2x + 1

Combining like terms:

28x = 21

Finally, we solve for x:

x = 21/28

Simplifying further:

x = 3/4

So, x = 3/4. Remember, laughter is the best solution to any equation!

Answer 7

[AI-generated answer — Explain Bot]

To solve the given equation log10(2x+1) - log10(3x-2) = 1 for x, we can use the properties of logarithms to simplify the equation and isolate x.

Step 1: Combine the logarithms using the quotient rule:
log10((2x+1)/(3x-2)) = 1

Step 2: Rewrite the equation in exponential form:
(2x+1)/(3x-2) = 10^1

Step 3: Simplify the right side of the equation:
(2x+1)/(3x-2) = 10

Step 4: Cross-multiply to eliminate the denominator:
2x + 1 = 10(3x-2)

Step 5: Distribute 10 on the right side:
2x + 1 = 30x - 20

Step 6: Rearrange the equation by moving all terms involving x to one side:
2x - 30x = -20 - 1

Step 7: Combine like terms:
-28x = -21

Step 8: Divide by -28 to solve for x:
x = (-21)/(-28)

Step 9: Simplify the fraction:
x = 3/4

So, the solution to the equation log10(2x+1) - log10(3x-2) = 1 is x = 3/4.