Solve for equation x. 3In(x)+2In(4)=In(128)

1 answer:

3 0

$Domain:\ x > 0\\\\3\ln(x)+2\ln(4)=\ln(128)\qquad\text{use}\ \lag_ab^n=n\log_ab\\\\\ln(x^3)+\ln(4^2)=\ln(128)\qquad\text{use}\ \log_ab+\ln_ac=\ln_a(bc)\\\\\ln(16x^3)=\ln(128)\iff16x^3=128\qquad\text{divide both sides by 16}\\\\x^3=8\to x=\sqrt[3]8\\\\\boxed{x=2}\in D$

You might be interested in

Convert 1400 pounds into kilograms. Round your answer to the nearest whole

jasenka [17]

Answer:

635 (635.0293 not rounded)

8 0

3 years ago

Kalsom answers 25 questions in math tests. He scored 81% to 93%. Calculate all possible number of questions successfully answere

cricket20 [7]

Answer:

21 and 22

Step-by-step explanation:

Let's work backward from that 81%: x/25 = 0.81 yields x = 20.25. Nominally, 20.25 / 25 = 0.81, but x must be an integer. Let's round 20.25 off to 20.

Thus, if Kalsom got 81%, it was a result of his having done 20 questions correctly.

81% corresponds to 20 questions correct;

82% to 20.5 questions correct, or, rounding up, to 21 questions correct;

83% to 20.75, or 21;

84% to 21 questions correct; this is the only result that makes sense (whole number of questions answered correctly)

85% to 21.25;

86% to 21.5;

87% to 21.75;

88% to 22 questions correct (this makes sense, unlike the last three)

89% to 22.25;

90% to 22.5;

91% to 22.75;

Assuming that the number of questions correct MUST be integer, then the possible number correct are 21 and 22, corresponding to 84% and 88% respectively.

4 0

4 years ago

Solve for x ....... thanks !

Len [333]

If we can match teh bases we can solve
because if x=x and xᵃ=xᵇ, we can conclude that a=b

16=2⁴
32=2⁵
rememeber that $(x^m)^n=x^{mn}$

$16^{3x+2}=32^{-2x-7}$
$(2^4)^{3x+2}=(2^5)^{-2x-7}$
$2^{4(3x+2)}=2^{5(-2x-7)}$
2=2 so we conclude that 4(3x+2)=5(-2x-7)

4(3x+2)=5(-2x-7)
expand/distribute
12x+8=-10x-35
add 10x both sides
22x+8=-35
minus 8 both sides
22x=-43
divide both sides by 22
x=-43/22

8 0

3 years ago

Does the graph represent y as a function of x?

Dimas [21]

Answer:

yes

Step-by-step explanation: i think cause the line is crossing both of the x and y axis

6 0

3 years ago

A bike was recently marked down $200.00 from its initial price. if you have a coupon for an additional 30% off after the markdow

love history [14]

Should be 525$ if I'm correct