Solve ln 5 + ln (2x) = 5. Round your answer to the nearest hundreth.
options
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A. 14.84
B. 11.17
C. 71.71
D. 0.02
Use the rules of logs
ln 5 + ln (2x) = 5
ln(5(2x)) = 5
ln (10x) = 5
10x = e^5
x = (1/10)e^5 = appr 14.84
Much easier to understand! Thank you @Reiny!
Did u already try to figure it out?
If not, try. Then post what you think the answer is.
I want to say "A".. or "C".. but my method to figuring it out, may be off.
@Damon
To solve the equation ln 5 + ln (2x) = 5, we can use properties of logarithms.
First, we can combine the two logarithms using the property of logarithms that states ln(a) + ln(b) = ln(a * b). Applying this property, we can rewrite the given equation as ln(5 * 2x) = 5.
Next, we can simplify the expression inside the logarithm by multiplying 5 and 2x to get ln(10x) = 5.
Now, we can convert the equation into exponential form. In general, if ln(x) = y, then e^y = x. Applying this to our equation, we get e^5 = 10x.
To solve for x, we divide both sides of the equation by 10: x = e^5/10 ≈ 14.778.
Rounding this answer to the nearest hundredth, we get x ≈ 14.78.
Therefore, the correct option is A. 14.84 (rounded to the nearest hundredth).