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Veronika [31]
4 years ago
8

Solve the equation by using tu basic properties of logarithms log(2x)=3 (Picture provided)

Mathematics
1 answer:
serg [7]4 years ago
7 0

Answer:

Option b

Step-by-step explanation:

According to the property of sum of logarithms we know that

log(ab) = log(a) + log(b).

In this case we have the equation:

log(2x) = 3

Using the property of sum of logarithms:

log(2) + log(x) = 3

log(x) = 3 - log(2)

We also know that:

10 ^{(logx)} = x     -------- <em>Inverse logarithm</em>

So:

x = 10 ^{3-log(2)}

x = 500

Another easiest way to solve it is the following:

Make w = 2x.

Then:

log(2x) = log(w)

log(w) = 3

w = 10^3  -------- <em>Inverse logarithm property</em>

w = 1000  

but w= 2x. Then:

2x = 1000\\\\x = 500

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