find ℒ{f(t)} by first using a trigonometric identity. (write your answer as a function of s.)
f(t) = 16cos(t−π/6)
ℒ{f(t)} = ?

Step-by-step explanation:

Given :

To find : ℒ{f(t)} by first using a trigonometric identity ?

Solution :

First we solve the function,

Applying trigonometric identity,

We know, and

Applying Laplace in function,

Therefore, The Laplace transformation is

you can't solve x because it is 2 linear equation and you only have one equation

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752