Question

Use natural logarithms to solve the equation. Round to the nearest thousandth. SHOW WORK

Answer 1

lne=1
2x+11=ln6
2x=ln6-11
x=(ln6-11)/2
x≈-4.6045e^(2x + 11)=30
divide by 5
e^(2x + 11)=6         is the answer hope i helpes
(2x+11)lne=ln6

Answer 2

Answer:

The value of x nearest to thousandth is, -4.6041

Step-by-step explanation:

Given the equation: $5e^{2x +11} = 30$

Use logarithmic rules:

$\log_b b = 1$

$\ln b^a = a \ln b$

Divide both sides by 5 we get;

$e^{2x+11} = 6$

Take log with base e both sides we get;

$\ln (e^{2x+11}) = \ln (6)$

Apply logarithmic rule;

$2x +11= 1.7917594692281$

Subtract 11 from both sides we get;

$2x = -9.20824053$

Divide both sides by 2 we get;

$x =-4.60412026$

Therefore, the value of x nearest to thousandth is, -4.604