Calcule o valor de x
a) ㏒^ 243 = 5
b) 2 ^ 4x-4 = 512
c) 5 ^ x = 1/625
d) 2 ^ 3x-9 = 64

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)

b)

c)

d)

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a)

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

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

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:

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

Add 4 on both sides:

Divide both sides by 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:

This implies .

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.

.

This implies:

Add 9 on both sides:

Divide both sides by 3:

Simplify:

here

step-by-step explanation: