Question

If characteristic of $log_{10} 0.00006$ is A and characteristic of $log_{3}750$ is B, then A + B is?
Please explain the answer. I will mark as brainliest.

Answer 1

$\underline { \pink { Characteristic \:of \:the \: logarithm }}$

Case 1:

The characteristic of the logarithm of a number having 'n' zeroes between the decimal sign and the first significant figure is -(n+1) .

$Here , log _{10} 0.00006$

$A = Chararecteristic \:of \: log _{10} 0.00006\\= -5$

$\underline { \pink { Characteristic \:of \:the \: logarithm }}$

Case 2:

The characteristic of the logarithm of a number greater than 1 is positive and is one less than the number of digits in the integral part of the number.

$log _{10} 750$

$B = Chararecteristic \:of \: log _{10} 750\\= 2$

$Now, \red { Value \:of \: A + B } \\= -5 + 2\\= -3$

Therefore.,

$\red { Value \:of \: A + B }\green {= -3}$

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Answer 2

Answer:

Step-by-step explanation:

log₁₀0.00006 = log₁₀(2*3*10⁻⁵)

= log₁₀(2)+log₁₀(3) + log₁₀(10⁻⁵)

=log₁₀(2)+log₁₀(3) -5

Characteristics = -5

A =  -5

log₃(750) = log₃(729+21)

= log₃(729(1+21/729))

=log₃(729) + log₃(1+21/729)

=log₃(3)⁶ + log₃(1+21/729)

= 6 + log₃(1+21/729)

Characteristics = 6

B = 6

A + B = -5 + 6 = 1