Question

If log x to the base 2 minus log 5 to the base 2 is equal to 3, find the value of x.

Answer 1

Answer:

Step-by-step explanation:

loga-logb=logab

so,

log(x/5)to base 2=3

x/5=2^3

x/5=8

x=40

Answer 2

Answer:

The value of $x$ is 40 in log₂x-log₂5=3

Step-by-step explanation:

Given :

The question which is given is that

$3$ is equal to $log x$ to the base $2$ minus $log 5$ to the base $2$.

To Solve:

The concept of logarithms will help us to solve this question and we need to find out the value of $x$ .
According to the above written format, we can arrange the expression as  :

$\log _2 x- \log _2 5 =3$

We know that $\log _a b=log(\frac{b}{a} )$

Now we can write the equation $\log _2 x- \log _2 5 = \log \left(\frac{x}{2}\right) - \log \left(\frac{5}{2}\right)$

Take LCM of the denominators and write $\frac{logx-log5}{log2}=3$

Now $logx=3log2+log5$

According to the logarithm's formula $alogb=logb^{a}$ and $log(ab)=loga+logb$

Therefore the expression will be :

$logx=log2^{3} +log5\\x=2^{3} \times 5\\x=40$

Thus the value of $x$ is 40  .

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