Can someone help solve this step by step
log2 4 + log2 (c-9) = 5
using the properties of logs,
log2 4 + log2 (c-9) = 5
log2 (4*(c-9)) = 5
4(c-9) = 2^5 = 32
4c-36 = 32
c = 17
check: log2(4)+log2(8) = 2+3 = 5
Sure, I can help you with that! But first, let me humor you a bit:
Why did the math book look sad?
Because it had too many problems! 📖😢
Now, let's solve the equation step by step.
We have the equation:
log2 4 + log2 (c-9) = 5
To combine the logs, we can use the property that says:
log(base a) x + log(base a) y = log(base a) (x * y)
Using this property, we can combine the two logarithms on the left-hand side of the equation:
log2 (4 * (c-9)) = 5
Simplifying further, we get:
log2 (4c - 36) = 5
To get rid of the logarithm, we can rewrite the equation in exponential form:
2^5 = 4c - 36
Simplifying the left-hand side, we have:
32 = 4c - 36
Now, let's solve for c:
32 + 36 = 4c
68 = 4c
c = 68/4
c = 17
Therefore, the solution to the equation log2 4 + log2 (c-9) = 5 is c = 17.
I hope that makes sense! Let me know if you have any further questions or if there's anything else I can do to bring a smile to your face. 😄
Certainly! I can help you solve this step by step.
The equation is log2 4 + log2 (c-9) = 5.
To solve it, we can use the logarithmic properties. The sum of logarithms can be expressed as the logarithm of the product of the numbers.
log2 4 + log2 (c-9) = log2(4 * (c-9))
Now we have:
log2(4 * (c-9)) = 5
To eliminate the logarithm, we need to change the equation into exponential form. In exponential form, the logarithm and the base are on the opposite sides:
2 ^ 5 = 4 * (c-9)
Simplifying the left side:
32 = 4 * (c-9)
Next, we can distribute the 4 on the right side:
32 = 4c - 36
Now, let's add 36 to both sides of the equation to isolate the variable term:
32 + 36 = 4c - 36 + 36
68 = 4c
Finally, divide both sides of the equation by 4 to solve for c:
68/4 = 4c/4
17 = c
So, the value of c that satisfies the equation log2 4 + log2 (c-9) = 5 is c = 17.
To solve the equation log2 4 + log2 (c-9) = 5 step by step, we can use the properties of logarithms.
Step 1: Combine the logs
Using the property loga x + loga y = loga (x * y), we can rewrite the equation as a single log expression:
log2 (4 * (c-9)) = 5
Step 2: Simplify the expression within the logarithm
The expression inside the logarithm can be simplified further by multiplying:
log2 (4c - 36) = 5
Step 3: Rewrite the equation in exponential form
Converting logarithmic equations to exponential form can help simplify the equation:
2^5 = 4c - 36
Step 4: Solve for c
Simplifying the exponential form gives us:
32 = 4c - 36
Step 5: Isolate the variable c
Adding 36 to both sides of the equation:
32 + 36 = 4c
68 = 4c
Step 6: Solve for c
Dividing both sides of the equation by 4:
68/4 = c
c = 17
So, the solution to the equation log2 4 + log2 (c-9) = 5 is c = 17.