All categories

2 years ago

Demonstrate two different ways to solve the equation 5^(2x+1) = 25.

Mathematics

1 answer:

Tanzania [10]2 years ago

3 0

Answer:

Step-by-step explanation:

Method 1: Taking the log of both sides...

So take the log of both sides...

5^(2x + 1) = 25

log 5^(2x + 1) = log 25 <-- use property: log (a^x) = x log a...

(2x + 1)log 5 = log 25 <-- distribute log 5 inside the brackets...

(2x)log 5 + log 5 = log 25 <-- subtract log 5 both sides of the equation...

(2x)log 5 + log 5 - log 5 = log 25 - log 5

(2x)log 5 = log (25/5) <-- use property: log a - log b = log (a/b)

(2x)log 5 = log 5 <-- divide both sides by log 5

(2x)log 5 / log 5 = log 5 / log 5 <--- this equals 1..

2x = 1

x=1/2

Method 2

5^(2x+1)=5^2

2x+1=2

2x=1

x=1/2

You might be interested in

The volume of a sphere is 904.32 cm3, find its radius and hence its curved surface area

Harlamova29_29 [7]

Volume = $\frac{4}{3}$ * π * r³ = 904.32 cm³

radius = $\sqrt[3]{\frac{3*Volume}{4 * pi} }$ cm=

= $\sqrt[3]{\frac{3 * 904.32}{4 * 3.14} }$ cm=

= $\sqrt[3]{\frac{2712,96}{12.56} }$ cm=

= $\sqrt[3]{216}$ cm=

radius = 6 cm

surface = 4 * π * r² cm² =

= 4 * π * 6² cm² =

= 4 * 3.14 * 36 cm² =

= 452,16 cm²

5 0

3 years ago

Solve for x in the diagram below 3x 80 2x

Vadim26 [7]

Answer:

x= 16

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Got a question on my math quiz asking the questions below. The question marked me as wrong, but didn’t tell me what I got wrong/

Vikki [24]

Answer:

1.33333... is a rational number because you know that the repeating part will all be 3 because it follows a pattern.

This is different from the first number because that repeating number does not have any identifiable pattern.

8 0

2 years ago

Please help me help my daughter with question number 9

butalik [34]

So in a division equation you would take the dividend then divide it by the divisor (which in this case would be the 2) then after you divided you would get your quotient

4 0

2 years ago

The sum of Jim's weight and Bob's weight is 180 pounds. If you subtract Jim's weight from Bob's weight, you get half of Bob's we

Furkat [3]

Answer:

120 pounds

Step-by-step explanation:

We can use systems of equations to solve this problem. Assuming j is Jim's weight and b is Bob's weight, the equations are:

j + b = 180

b - j = 1/2b

Let's get b - j = 1/2b into standard form (b, then j, then the equal sign, then the constant.)

$b - j = \frac{b}{2}\\\frac{b}{2} - j = 0$

Now we can solve using the process of elimination.

$b + j = 180\\\\\frac{b}{2} - j = 0\\\\b + \frac{b}{2} = 180\\\\b + b \cdot 2 = 180\cdot 2\\3b = 360\\b = 120$

Now we know how much Bob weighs, for fun, let's find Jim's weight by substituting into the equation.

$120 + j = 180\\j = 180-120\\j = 60$

So Bob weighs 120 pounds and Jim weight 60 pounds.

Hope this helped!

4 0

2 years ago

Read 2 more answers