anyone know how to solve this step by step?
e^(3ln2)
let x= e^ 3ln2
so lnx = ln (e^ 3ln2)
lnx = 3ln2(lne) but ln e = 1
so
ln x = 3ln 2
ln x = ln 2^3
ln x = ln 8
x = 8
so
e^(3ln2) = 8
To solve the expression e^(3ln2) step by step, we can use a property of logarithms and exponentials. Let's break it down:
Step 1: Rewrite the expression using the property log_a(b^c) = c * log_a(b):
e^(3ln2) = e^(ln2^3)
Step 2: Simplify the right side of the equation:
e^(ln2^3) = e^(ln8)
Step 3: Use the property e^(ln(x)) = x:
e^(ln8) = 8
Therefore, the solution to the expression e^(3ln2) is 8.
To solve the expression e^(3ln2) step by step, we can use the property of logarithms that states ln(a^b) = b * ln(a). Additionally, we can use the property of exponentials that states e^ln(a) = a.
1. Begin by simplifying the natural logarithm within the expression. ln(2) can be evaluated using a calculator or its approximate value of 0.693.
e^(3 * ln2) becomes e^(3 * 0.693)
2. Multiply the exponential and the logarithm. Since 3 and 0.693 are constants, their product is approximately 2.079.
e^(3 * 0.693) becomes e^(2.079)
3. Finally, evaluate e^(2.079) using a calculator or a mathematical approximation to obtain the final result.