Question

log x= 3log2 +log25− log20

Answer 1

$\texttt{\textsf{\large{\underline{Solution}:}}}$

Given:

• ㏒₁₀(x) = 3 ㏒₁₀(2) + ㏒₁₀(25) - ㏒₁₀(20)

To Find:

• The value of x ?

When no base is written, we assume that the base is 10.

Therefore,

→ ㏒₁₀(x) = 3 ㏒₁₀(2) + ㏒₁₀(25) - ㏒₁₀(20)

Using formula n ㏒(x) = ㏒(xⁿ) we get,

→ ㏒₁₀(x) = ㏒₁₀(2³) + ㏒₁₀(25) - ㏒₁₀(20)

→ ㏒₁₀(x) = ㏒₁₀(8) + ㏒₁₀(25) - ㏒₁₀(20)

Using formula ㏒(x) + ㏒(y) = ㏒(xy), we get,

→ ㏒₁₀(x) = ㏒₁₀(8 × 25) - ㏒₁₀(20)

→ ㏒₁₀(x) = ㏒₁₀(200) - ㏒₁₀(20)

Using formula ㏒(x) - ㏒(y) = ㏒(x/y), we get,

→ ㏒₁₀(x) = ㏒₁₀(200/20)

→ ㏒₁₀(x) = ㏒₁₀(10)

Comparing both side, we get,

→ x = 10

Δ So, the value of x is 10.

$\texttt{\textsf{\large{\underline{Answer}:}}}$

• x = 10.

•••♪