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3 years ago

How do you convert powers to the same base if the bases don't have common factors?

Mathematics

1 answer:

Yuri [45]3 years ago

8 0

Answer:

6²

Step-by-step explanation:

Use the rule of exponents ...

(a·b)^c = a^c·b^c

Your expression has a=3, b=2, c=2.

3²·2² = (3·2)² = 6²

_____

If you want to get more sophisticated than that, logarithms can get involved.

$3^2\cdot 2^2=10^{2\log{(3)}+2\log{(2)}}\approx 10^{1.5563025}$

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Write y=10x as a logarithmic function please

Margaret [11]

$\bf \textit{exponential form of a logarithm}
\\\\
log_a b=y \implies a^y= b\qquad\qquad 
% exponential notation 2nd form
a^y= b\implies log_a b=y \\\\
-------------------------------\\\\
y=10^x\implies log_{10}(y)=x$

5 0

3 years ago

Find the solutions to 9x^2-54x=0

astra-53 [7]

Answer:

x₁ = 0

x₂ = 6

Step-by-step explanation:

9x² - 54x = 0

9x(x - 6) = 0

x(x - 6) = 0

x = 0

x - 6 = 0 → x = 6

Hope this helps! :)

7 0

3 years ago

Read 2 more answers

Solve each system of equations by writing a new system that eliminates one of the variables.

Rufina [12.5K]

Answer:

$x=33\\y=-41$

Step-by-step explanation:

Let:

$2x+y=25\hspace{5}(1)\\and\\4x+3y=9\hspace{5}(2)$

We need to eliminate one of the variables, so let's use elimination method. First multiply (1) by 2

$2*(1)\equiv\hspace{5}4x+2y=50$

Now subtract (2) from 2*(1) in order to eliminate x:

$2*(1)-(2)\\4x-4x+2y-3y=50-9\\-y=41$

Solving for y:

Multiplying both sides by -1

$y=-41$

Finally, replacing the value of y in (1)

$2x-41=25$

Solving for x:

add 41 to both sides:

$2x=66$

Multiply both sides by 1/2:

$x=\frac{66}{2} =33$

3 0

3 years ago

If the simple interest on $4,000 for 10 years is $3,200,then what is the interest rate

STALIN [3.7K]

The answer will be 1.25

3 0

3 years ago

Read 2 more answers

Write your answer as a mixed number in simplest form

Neko [114]

Answer:

2 5/12

Step-by-step explanation:

You put it so that the denominators are the same so in this case I used 12 as the denominator and used the rule for each. Next I subtracted 3 9/12 minus 1 4/12 and got 2 5/12

5 0

3 years ago