Evaluate 6log(x+4)=log64
6log(x+4)=log64 , initial condition: x > -4
log ( (x+4)^6 ) = log 64
(x+4)^6 = 64
take 6th root of both sides
x+4 = ± 2
x = -6 or x = -2
but x > -6, so .... x = -2
Well, if we can find the value of x that satisfies the equation, we can evaluate whether the equation is true or false!
Let's start by simplifying the equation. We know that log64 is equal to 6 because 64 to the power of 6 is, well, 64! So we can rewrite the equation as:
6log(x+4) = 6
Dividing both sides by 6, we get:
log(x+4) = 1
Now, since we're dealing with logarithms, we can rewrite this equation using exponentiation:
10^1 = x+4
Simplifying further, we find:
10 = x+4
Here we have a classic math puzzle: Where in the world is x? 🌎
To solve this, we simply subtract 4 from both sides of the equation:
10 - 4 = x
And voila! We find that x = 6.
So, the value of x that satisfies the equation is 6.
To evaluate the equation 6log(x+4) = log64, we need to solve for x.
Step 1: Use the property of logarithms that states log(a^b) = b * log(a) to rewrite the equation.
6log(x+4) = log64 can be rewritten as:
log((x+4)^6) = log64
Step 2: Since the logarithm function is one-to-one, we can remove the logarithm from both sides of the equation.
(x+4)^6 = 64
Step 3: Take the sixth root of both sides of the equation to isolate x.
∛((x+4)^6) = ∛64
Simplifying, we get:
x+4 = 4
Step 4: Subtract 4 from both sides of the equation to solve for x.
x = 4 - 4
x = 0
Therefore, the solution to the equation 6log(x+4) = log64 is x = 0.
To evaluate the equation 6log(x+4) = log64, we need to solve for the value of x.
First, let's simplify the equation by using logarithmic properties. One of the properties states that log(a^b) = b * log(a). Applying this property, we can rewrite log64 as log(2^6) = 6 * log2.
So the equation becomes 6log(x+4) = 6 * log2.
Now, we can cancel out the common factor of 6 on both sides of the equation:
log(x+4) = log2.
Now, to solve for x, we need to get rid of the logarithm by exponentiating both sides with the base of the logarithm, which is 10:
10^(log(x+4)) = 10^(log2).
By the logarithm and exponentiation being inverse operations, they cancel each other out, leaving us with:
x + 4 = 2.
Finally, solve for x by subtracting 4 from both sides of the equation:
x = 2 - 4 = -2.
Therefore, the value of x that satisfies the equation 6log(x+4) = log64 is x = -2.