ln(e^(5)·3^log3(e)+1/2e^-3ln(2)
the first base e has en exponent of 5 times 3 to the power/exponent of log with a base of 3 (3). the second base of e has a power/exponent of (-3In(2)
recall that
log_a(b) = 1/log_b(a)
so, your expression is
ln(e^5) + ln(e) + (1/2)(1/8))
= 5+1+1/16
= 97/16
To solve this expression, let's break it down step by step:
Step 1: Rewrite the expression
ln(e^(5)·3^log3(e)+1/2e^-3ln(2))
Step 2: Simplify the inner expression
e^(5) can be simplified to e * e * e * e * e
3^log3(e) simplifies to e
e^-3ln(2) can be written as 1/(e^3ln(2))
Step 3: Substitute the simplified values back into the original expression
ln(e * e * e * e * e * e * e + 1/2 * 1/(e^3ln(2)))
Step 4: Combine the like terms and simplify further if necessary
ln(e^7 + 1/(2e^3ln(2)))
And that is the simplification of the given expression step-by-step.