Question

If log3 x logy 3 log2 y = 5, then x =​

Answer 1

Answer:

Logarithm definition

When b is raised to the power of y is equal x:

b y = x

Then the base b logarithm of x is equal to y:

logb(x) = y

For example when:

24 = 16

Then

log2(16) = 4

Logarithm as inverse function of exponential function

The logarithmic function,

y = logb(x)

is the inverse function of the exponential function,

x = by

So if we calculate the exponential function of the logarithm of x (x>0),

f (f -1(x)) = blogb(x) = x

Or if we calculate the logarithm of the exponential function of x,

f -1(f (x)) = logb(bx) = x

Natural logarithm (ln)

Natural logarithm is a logarithm to the base e:

ln(x) = loge(x)

When e constant is the number:

e=\lim_{x\rightarrow \infty }\left ( 1+\frac{1}{x} \right )^x = 2.718281828459...

or

e=\lim_{x\rightarrow 0 }\left ( 1+ \right x)^\frac{1}{x}

 

See: Natural logarithm

Inverse logarithm calculation

The inverse logarithm (or anti logarithm) is calculated by raising the base b to the logarithm y:

x = log-1(y) = b y

Logarithmic function

The logarithmic function has the basic form of:

f (x) = logb(x)

Answer 2

Correct Question

If $log_{3} x\ log_{y} 3\ log_{2} y=5$, then x =​

Answer:

The value of x is 32.

Step-by-step explanation:

Given:

$log_{3} x\ log_{y} 3\ log_{2} y=5$

To Find:

The value of x .

Formula Used:

$log_{p} q=\frac{log\ p\ }{log\ q}$  ------------- formula no.01.

$p\ log q= logq^{p}$   ------------- formula no.02

Solution:

As given- $log_{3} x\ log_{y} 3\ log_{2} y=5$.

$log_{3} x\ log_{y} 3\ log_{2} y=5$

Applying formula no.01.

$\frac{logx}{log3} \times\frac{log3}{logy} \times\frac{logy}{log2}=5$

$\frac{logx}{log2} =5$

$logx=5 log2$

Applying formula no.02.

$logx=log2^{5}$

$x=2^{5}$

$x=32$

Thus,the value of x is 32.

PROJECT CODE #SPJ3