Ask question

Ask question

All categories

3 years ago

6

Select all of the potential solution(s) of the equation 2log5x=log54.

2 answers:

Ilya [14]3 years ago

8 0

X= -2 and x= 2 are the answers

sergij07 [2.7K]3 years ago

3 0

Given : $2log_{5} x^{2} =log_{5} 2^{2}$

To solve for x we use the logarithm rule for powers.

The log rule for powers states:

$mlog_{a}n =log_{a} n^{m}$

We apply this rule to the left side of the equation.

[tex] log_{5} x^{2} =log_{5} 4

Both sides have log with same base so it can be eliminated.

Eliminating log from both sides we have:

[tex] x^{2} =4

To solve for x we take root of both sides

x=2,-2.

You might be interested in

Are parallelograms always squares.

DerKrebs [107]

A parallelogram<span> is a four-sided figure with two sets of parallel sides. This is </span>always true<span>. </span>Squares<span> are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. </span>Parallelograms<span> are quadrilaterals with two sets of parallel sides.</span>

5 0

3 years ago

The owner of a movie theater wants to survey theater customers about their favorite types of movies.

Nutka1998 [239]

C) 50 randomly selected people leaving the movie teather

4 0

3 years ago

Read 2 more answers

if the x intercept of a line is positive and the y intercept is negative, does the line slant upwards or downwards from left to

Zigmanuir [339]

From left to right, the line slants upwards like in this image:

5 0

3 years ago

For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4

Elina [12.6K]

Answer:

<em>C.</em> $(5-\frac{1}{2})^6$

Step-by-step explanation:

Given

$15(5)^2(-\frac{1}{2})^4$

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

$Sum = 2 + 4$

$Sum = 6$

Each term of a binomial expansion are always of the form:

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

Where n = the sum above

$n = 6$

Compare $15(5)^2(-\frac{1}{2})^4$ to the above general form of binomial expansion

$(a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......$

Substitute 6 for n

$(a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......$

[Next is to solve for a and b]

<em>From the above expression, the power of (5) is 2</em>

<em>Express 2 as 6 - 4</em>

$(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......$

By direct comparison of

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

and

$(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......$

We have;

$^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4$

Further comparison gives

$^nC_r = 15$

$a^{n-r} =(5)^{6-4}$

$b^r= (-\frac{1}{2})^4$

[Solving for a]

By direct comparison of $a^{n-r} =(5)^{6-4}$

$a = 5$

$n = 6$

$r = 4$

[Solving for b]

By direct comparison of $b^r= (-\frac{1}{2})^4$

$r = 4$

$b = \frac{-1}{2}$

Substitute values for a, b, n and r in

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

$(5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......$

Solve for $^6C_4$

$(5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......$

<em>Check the list of options for the expression on the left hand side</em>

<em>The correct answer is </em> $(5-\frac{1}{2})^6$ <em />

3 0

3 years ago

Which characteristics best describe a right scalene triangle? I. Two sides meet at a 90° angle. II. Two side lengths are equal.

Alisiya [41]

Answer:

1

1V

Step-by-step explanation:

8 0

3 years ago