Question

Simplify:
$\log_{10} 3 + \log_{10} 2 - 2\log_{10} 5$

Answer 1

Answer:

log₁₀(6/25)

Step-by-step explanation:

Hi,

We will be using the following properties of

logarithm:

Additive Property : logₐx + logₐy = logₐ(xy) ,

Subtraction Property : logₐx - logₐy = logₐ(x/y)and

Exponent Property : nlogₐx = logₐxⁿ

Consider L.H.S

= log₁₀3 + log₁₀2 - 2log₁₀5

log₁₀3 + log₁₀2 = log₁₀(3*2) = log₁₀6

(Using Additive Property)

2log₁₀5 = log₁₀5² = log₁₀25

(Using Exponent Property)

L.H.S

= log₁₀6 - log₁₀25

(Using Subtraction Property)

= log₁₀(6/25)

Hope, it helps !