how do solve for x 2.3^x=81-3^x
To solve the equation 2.3^x = 81 - 3^x for x, we can use logarithms. Here's the step-by-step process:
Step 1: Rearrange the equation to isolate one of the exponential terms. In this case, let's isolate 3^x:
2.3^x = 81 - 3^x
2.3^x + 3^x = 81
Step 2: Simplify the equation by converting the base 3 term to base 2.3 term:
(2.3^x) * (1 + (3/2.3)^x) = 81
Step 3: Take the logarithm of both sides of the equation to bring down the exponent:
log((2.3^x) * (1 + (3/2.3)^x)) = log(81)
log(2.3^x) + log(1 + (3/2.3)^x) = log(81)
Step 4: Use the logarithmic property that states log(a^b) = b * log(a):
x * log(2.3) + log(1 + (3/2.3)^x) = log(81)
Step 5: Solve for x using numerical methods (e.g., graphing calculator, Newton's method, etc.), as the equation now contains both logarithmic and exponential terms.
Note: While it is possible to simplify the equation further using properties of logarithms, it wouldn't result in an algebraic solution for x.
2.3^x + 3^x = 81 --- that would be a tough one.
Wolfram gave me this:
http://www.wolframalpha.com/input/?i=2.3%5Ex+%2B+3%5Ex+%3D+81
I will assume you meant to type:
2.
3^x = 81 - 3^x
2(3^x) = 81
take log of both sides and use rules of logs
log 2 + xlog3 = log81
x = (log81 - log2)/log3 = appr 3.369
otherwise, retype the equation in its proper form