wats the positive root of the equation
x^-3x=10?
To find the positive root of the equation x^(-3x) = 10, we need to solve for x.
Step 1: Rewrite the equation using exponents:
1/x^(3x) = 10
Step 2: Take the reciprocal of both sides to remove the negative exponent:
x^(3x) = 1/10
Step 3: Rewrite 1/10 as a decimal:
x^(3x) = 0.1
Step 4: Take the logarithm of both sides using any base, such as the natural logarithm (ln) or common logarithm (log):
ln(x^(3x)) = ln(0.1)
Step 5: Apply the logarithm rules to bring down the exponent:
3x * ln(x) = ln(0.1)
Step 6: Divide both sides of the equation by 3 to isolate the variable:
x * ln(x) = ln(0.1) / 3
Step 7: Use numerical methods, such as graphing or Newton's method, to approximate the value of x. Since there is no algebraic way to find a precise solution in this case, we can use a calculator or software to estimate the value.
Alternatively, you can use an online solver or software to directly solve the equation for you by plugging in the equation x^(-3x) = 10 and finding the positive root.