Question

please answer the above...
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Answer 1

Step-by-step explanation:

$\sf {log}_{2}{{log}_{4}{({log}_{10}{{16}^{4}} + {log}_{10}{{25}^{8}})}} \\ \\ \sf = {log}_{2}{{log}_{4}{({4{log}_{10}{16} + 8{log}_{10}{25})}}} \\ \\ \sf = {log}_{2}{{log}_{4}{(4{log}_{10}{{4}^{2}}+ 8{log}_{10}{25})}}} \\ \\ \sf = {log}_{2}{{log}_{4}{(8{log}_{10}{4} + 8{log}_{10}{25})}}} \\ \\ \sf = {log}_{2}{{log}_{4}{8({log}_{10}{4} + {log}_{10}{25})}}} \\ \\ \sf = {log}_{2}{{log}_{4}{8{log}_{10}{(25 \times 4)}}}} \\ \\ \sf = {log}_{2}{{log}_{4}{8{log}_{10}{100}}}} \\ \\ \sf = {log}_{2}{{log}_{4}{16}}} \\ \\ \sf = {log}_{2}{2} \\ \\ \sf = 1 \\ \\ \sf Some\: properties\:of \: logarithm \\ \\ \sf {log}_{x}{a} + {log}_{x}{b} = {log}_{x}{ab} \\ \\ \sf {log}_{x}{a} - {log}_{x}{b} = {log}_{x}{\frac{a}{b}} \\ \\ \sf {log}_{x}{1}=0 \\ \\ \sf {log}_{x}{{m}^{n}} = n{log}_{x}{m} \\ \\ \sf {log}_{x}{{x}^{n}} = n$

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Answer 2

Answer:

10.) 1

11.) 2.4846 (approx.)

= 2.48456245

Step-by-step explanation:

★ NOTE : THE EXPLANATION OF THE QUESTIONS IS GIVEN IN THE ATTACHMENTS ABOVE. KINDLY REFER TO THEM.

• ATTACHMENT 1 = Answer 10 (starting)

• ATTACHMENT 2 = Answer 10 (ending)

• ATTACHMENT 3 = Answer 11 (starting)

• ATTACHMENT 4 = Answer 11 (continuation)

• ATTACHMENT 5 = Answer 11 (ending)

★ 'A piece of Supplementary Counsel' :-

• Natural Logarithm = The natural logarithm has base e, a famous irrational number, and is represented on the calculator by ln(x). The natural and common logarithm can be found throughout Algebra and Calculus. Defines common log, log x, and natural log, ln x, and works through examples and problems using a calculator.

• Logarithm = The logarithm of any number to given base is the power to which base must be raised to obtain that number.

In general, if N = a^x , then, loga(N) = x

• Some properties :-

➡ 1000 = 10^3 : log10(1000) = 3

➡ a^0 = 1 : loga(1) = 0

➡ a^1 = a : loga(a) = 1

• Logarithmic Formulae -

• Product Formula :

loga(m) + loga(n) = loga(mn)

• Quotient Formula :

loga(m) - loga(n) = loga(m/n)

• Power Formula :

loga(m^n) = n•loga(m)

• Base change Formula :

loga(m) = logb(m) × loga(b)