6^(x-36)=52
solve for x
This requires logarithms
take log of both sides
log[6^(x-36)] = log 52
(x-36)log 6 = log 52
x-36 = log52/log6
x = log52/log6 + 36
I will let you do the button-pushing.
X=38.21
To solve the equation 6^(x-36) = 52 for x, you need to isolate the variable x. Here's how you can approach it:
Step 1: Take the logarithm of both sides
Applying a logarithm to both sides of the equation can help to eliminate the exponent. You can use any logarithm base; however, let's use the natural logarithm (ln) for this explanation.
Taking the natural logarithm of both sides gives:
ln(6^(x-36)) = ln(52)
Step 2: Apply the logarithmic property
Using the logarithmic property, the exponent (x - 36) can be brought down as a coefficient:
(x - 36) * ln(6) = ln(52)
Step 3: Solve for x
Now, you just need to isolate x. Start by dividing both sides of the equation by ln(6):
x - 36 = ln(52) / ln(6)
Step 4: Add 36 to both sides to solve for x
x = ln(52) / ln(6) + 36
Using a calculator, evaluate the right side of the equation to find the numerical value of x.