What is the solution to the equation below? Round your answer to two decimal places? (apex) 5+8*In x=15.8
A: x=3.86
b:x=2.26
c:x=0.30
d:x=3.67

Option A : is the solution of the equation.

Explanation:

The equation is

To determine the value of x, let us simplify the equation.

Subtracting 5 from both sides of the equation, we have,

Simplifying, we get,

Now , dividing both sides of the equation by 8, we get,

Using the logarithmic definition that if then

Thus, rewriting the above expression using the logarithmic definition, we have,

⇒

Substituting the value of , we get,

Rounding off the answer to two decimal places, we get,

Hence, the solution of the equation is

Therefore, Option A is the correct answer.

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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