Solve -- 23*2^3x=40
assuming you meant:
23*2^(3x) = 40
2^(3x) = 40/23
take log of both sides and use log rules
3x log2 = log40 - log23
x = (log40 - log23)/(3log2) = appr. ......
23*2^3x = 40.
2^3x = 40/23 = 1.739
3x*Log2 = Log1.739
3x = 0.7984
X = 0.26613.
To solve the equation 23 * 2^(3x) = 40, we need to isolate the variable x.
Step 1: Divide both sides of the equation by 23 to get rid of the coefficient on the left side.
(23 * 2^(3x))/23 = 40/23
2^(3x) = 40/23
Step 2: Take the logarithm of both sides of the equation. Any base can be used, but it is common to use base 10 or base e (natural logarithm).
log(2^(3x)) = log(40/23)
Step 3: Apply the exponent property of logarithms to bring down the exponent in front.
(3x)log(2) = log(40/23)
Step 4: Divide both sides of the equation by log(2) to isolate the variable x.
3x = log(40/23)/log(2)
Step 5: Divide both sides of the equation by 3 to solve for x.
x = log(40/23)/(3*log(2))
Now, you can use a calculator or software to evaluate the expression on the right-hand side to find the value of x.