I'm doing logarithms.
Solve: 2^(6x-1)=28
To solve the equation 2^(6x-1) = 28 for x, we need to use logarithms. Specifically, we will use the logarithm base 2 since the base of the exponent in the equation is 2.
Here's how to solve it step by step:
Step 1: Take the logarithm of both sides of the equation using the base 2:
log2(2^(6x-1)) = log2(28)
Step 2: Apply the logarithmic property that states log(base a)(a^b) = b. This will eliminate the exponent on the left side:
(6x-1)log2(2) = log2(28)
Since log2(2) = 1, the equation becomes:
6x - 1 = log2(28)
Step 3: Now, isolate x by moving the constant term to the other side of the equation:
6x = log2(28) + 1
Step 4: Finally, divide both sides of the equation by 6 to solve for x:
x = (log2(28) + 1) / 6
Now, you can use a calculator or software to evaluate the right side of the equation to obtain the numerical value of x.