Question

Calcule o valor de x

Answer 1

Answer:

a)3

b)13/4

c)-4

d)5

NOTE:  You might want to read the first section below the "Step-by-step explanation:" to see if I have interpreted your problems correctly.

Step-by-step explanation:

a)

$\log_x(243)=5$

b)

$2^{4x-4}=512$

c)

$5^x=\frac{1}{625}$

d)

$2^{3x-9}=64$

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a)

Let's writ ether the logarithmic form in equivalent exponential form:

$x^5=243$

To solve this we need to take the fifth root of both sides:

$x=243^\frac{1}{5}$

$x=3$

b)

We are going to write both sides so their bases are 2.

The left hand side is already base 2 so we are not doing anything to that side.

The 512 however can be written as 2^9.

So we have:

$2^{4x-4}=2^{9}$

Since the bases are the same, the only thing we can do is set the exponents equal so those are the same as well.

$4x-4=9$

Add 4 on both sides:

$4x=13$

Divide both sides by 4:

$x=\frac{13}{4}$

c)

We are going to write both sides so their bases are 5.

This does not effect left hand side since the base is already 5 on that side.

I know 5^4=625 so 5^(-4)=1/625.

So we have:

$5^x=5^{-4}$

This implies $x=-4$.

d)

We are going to write both sides so they have base 2.

Left hand side is done. Let's move on to the right. 64=2^6.

$2^{3x-9}=2^6$.

This implies:

$3x-9=6$

Add 9 on both sides:

$3x=15$

Divide both sides by 3:

$x=\frac{15}{3}$

Simplify:

$x=5$