log6(x+7)−log6x=2

Solve for x

loga- logb= log (a/b)

log6 ((x+7)/x)=2
(x+7)/x=36

can you do it from here?

Log6((x+7)/x)=2

is 6^2=x+7/x
is 36=x/x+7/x and x/x=1
36=1+7/x
36-1=1-1+7/x
35=7/x
x=7/35 reduces to x=1/5

Why did the logarithm go to the circus? Because it wanted to solve some tricky equations! Let's solve this one together.

Using the property of logarithms, we can combine the two logarithms into a single one:

log6((x + 7)/x) = 2

To get rid of the logarithm, we can rewrite it in exponential form:

6^2 = (x + 7)/x

36 = (x + 7)/x

Now, let's multiply both sides by x to eliminate the fraction:

36x = x + 7

Brace yourself, it's math time! Subtract x from both sides:

35x = 7

And finally, divide both sides by 35:

x = 7/35

Simplifying that, we get:

x = 1/5

So, the solution to the equation is x = 1/5. Now that's a mathlete's dream come true!

To solve the equation log6(x+7) - log6x = 2, we can use the properties of logarithms.

Step 1: Combine the logarithms using the quotient rule:
log6[(x+7)/x] = 2

Step 2: Rewrite the equation in exponential form:
6^2 = (x+7)/x

Step 3: Simplify the exponent:
36 = (x+7)/x

Step 4: Multiply through by x to eliminate the fraction:
36x = x + 7

Step 5: Subtract x from both sides:
36x - x = 7

Step 6: Simplify the equation:
35x = 7

Step 7: Divide both sides by 35 to solve for x:
x = 7/35

Step 8: Simplify the fraction:
x = 1/5

Therefore, the solution to the equation log6(x+7) - log6x = 2 is x = 1/5.

To solve the equation log6(x+7) - log6x = 2 for x, we can use the properties of logarithms and algebraic manipulation. Here's a step-by-step solution:

Step 1: Combine the logarithmic terms using the quotient rule of logarithms, which states that logb(a) - logb(c) = logb(a/c).

log6(x+7) - log6x = log6((x+7)/x) = 2

Step 2: Rewrite the equation using the exponential form of logarithms. In exponential form, logb(x) = y is equivalent to b^y = x.

6^2 = (x+7)/x

Step 3: Simplify the equation.

36 = (x+7)/x.

Step 4: Multiply both sides of the equation by x to eliminate the fraction.

36x = x + 7.

Step 5: Move all terms involving x to one side of the equation and simplify.

36x - x = 7.

35x = 7.

Step 6: Divide both sides of the equation by 35 to solve for x.

x = 7/35.

Step 7: Simplify the result.

x = 1/5.

So, the solution to the equation log6(x+7) - log6x = 2 is x = 1/5.