 Recent questions in Logarithms Antinazius 2021-11-07 Answered

### Compound interest Solve the compound interest formula $$\displaystyle{A}={P}{\left({1}+{\frac{{{r}}}{{{n}}}}\right)}^{{{n}{t}}}$$ for t by using natural logarithms Caelan 2021-11-07 Answered

### Explain how you would solve the following equation: $$\displaystyle{\ln{{\left({x}\right)}}}+{\ln{{\left({x}−{5}\right)}}}={\ln{{\left({21}−{x}\right)}}}$$ Describe why you may only choose some of the possible roots of any polynomial you reduce the problem to Step 1 By using the property of logarithms, simplify the LHS . $$\displaystyle{\ln{{\left({a}\right)}}}+{\ln{{\left({b}\right)}}}={\ln{{\left({a}{b}\right)}}}$$ $$\displaystyle\text{Simplify the LHS}$$ $$\displaystyle{\ln{{\left({x}\right)}}}+{\ln{{\left({x}-{5}\right)}}}={\ln{{\left({x}{\left({x}-{5}\right)}\right)}}}$$ $$\displaystyle={\ln{{\left({x}^{{2}}-{5}{x}\right)}}}$$ Step 2 Since there is log term on both the sides of the equation, we can take antilog on both sides, simplify and solve the quadratic for x $$\displaystyle{\ln{{\left({x}^{{2}}-{5}{x}\right)}}}={\ln{{\left({21}-{x}\right)}}}$$ $$\displaystyle{e}^{{{\ln{{\left({x}^{{2}}-{5}{x}\right)}}}}}={e}^{{{\ln{{\left({21}-{x}\right)}}}}}$$ $$\displaystyle{x}^{{2}}-{5}{x}={x}-{21}$$ $$\displaystyle{x}^{{2}}-{5}{x}-{x}-{21}={0}$$ $$\displaystyle{x}^{{2}}-{4}{x}-{21}={0}$$ $$\displaystyle{x}^{{2}}-{7}{x}+{3}{x}-{21}={0}$$ $$\displaystyle{x}{\left({x}-{7}\right)}+{3}{\left({x}-{7}\right)}={0}$$ $$\displaystyle{\left({x}-{7}\right)}{\left({x}+{3}\right)}={0}$$ $$\displaystyle\Rightarrow{x}={7},{x}=-{3}$$ Step 3 There are two solutions possible for value of x, one positive the other negative. However notice that in the given question there is a term ln(x). But since log of a number is defined only for x>0, we discard x=-3. Hence the answer is x=7. sanuluy 2021-11-07 Answered

### Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. $$\displaystyle{2}{{\log}_{{5}}{\left({x}-{3}\right)}}-{{\log}_{{58}}=}{{\log}_{{52}}}$$ babeeb0oL 2021-11-07 Answered

### Solve for (y) in terms of (x): $$\displaystyle{3}{\ln{{y}}}={3}{\ln{{x}}}$$ floymdiT 2021-11-07 Answered

### Solve the exponential equation $$\displaystyle{e}^{{{4}{x}-{5}}}-{7}={11243}$$. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. Emily-Jane Bray 2021-11-07 Answered

### Use the Laws of Logarithms to evaluate the expression. $$\displaystyle{{\log}_{{3}}{\left({15}\right)}}-{{\log}_{{3}}{\left({40}\right)}}+{{\log}_{{3}}{\left({216}\right)}}$$ skeexerxo175o 2021-11-06 Answered

### Solve the logarithmic equation $$\displaystyle{\ln{{\left({x}-{4}\right)}}}+{\ln{{\left({x}+{1}\right)}}}={\ln{{\left({x}-{8}\right)}}}$$. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation,correct to two decimal places, for the solution. kdgg0909gn 2021-11-06 Answered

### Use the properties of logarithms to expand the quantity. $$\displaystyle{\ln{{\frac{{{x}^{{2}}}}{{{\left({y}^{{3}}{z}^{{4}}\right)}}}}}}$$ Charles Cisneros 2021-11-06 Answered

### Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. $$\displaystyle{\log{{\left({x}-{1}\right)}}}={\left({\frac{{{1}}}{{{3}}}}\right)}{\log{{2}}}$$ Sherry Becker 2021-11-06 Answered

### Write the expression as a logarithm: $$\displaystyle{2}{{\log}_{{2}}{\left({x}-{3}\right)}}+{{\log}_{{2}}{\left({2}{x}+{3}\right)}}$$ permaneceerc 2021-11-06 Answered

### Use the Laws of Logarithms to expand the expression. $$\displaystyle{{\log}_{{3}}{\left({x}\sqrt{{y}}\right)}}$$ Trent Carpenter 2021-11-06 Answered

### Write the expression as one logarithm . SNIPP $$\displaystyle{\log{{\left({x}^{{3}}{y}^{{2}}\right)}}}-{2}{\log{{x}}}\sqrt{{{3}}}{\left\lbrace{y}\right\rbrace}-{3}{\log{{\left({\frac{{{x}}}{{{y}}}}\right)}}}$$ Zoe Oneal 2021-11-06 Answered

### Given that $$\displaystyle{{\log}_{{a}}{\left({5}\right)}}\approx{0.65}$$ and $$\displaystyle{{\log}_{{a}}{\left({3}\right)}}\approx{0.44}$$, evaluate each of the following. Hint: use the properties of logarithms to rewrite the given logarithm in terms of the logarithms of 5 and 3 a)$$\displaystyle{{\log}_{{a}}{\left({0.6}\right)}}$$ b)$$\displaystyle{{\log}_{{a}}{\left(\sqrt{{3}}\right)}}$$ c)$$\displaystyle{{\log}_{{a}}{\left({15}\right)}}$$ d)$$\displaystyle{{\log}_{{a}}{\left({25}\right)}}$$ e)$$\displaystyle{{\log}_{{a}}{\left({75}\right)}}$$ f)$$\displaystyle{{\log}_{{a}}{\left({1.8}\right)}}$$ Line 2021-11-06 Answered

### Evaluate $$\displaystyle{{\log}_{{580}}}$$ sjeikdom0 2021-11-06 Answered

### Solve $$\displaystyle{{\log}_{{{10}}}{210}}$$ chillywilly12a 2021-11-06 Answered

### Describe the power rule for logarithms and give an example. boitshupoO 2021-11-06 Answered

### Write the equation in its equivalent exponential form. $$\displaystyle{4}={{\log}_{{5}}{M}}$$ Jaya Legge 2021-11-05 Answered

### Use the properties of logarithms to expand the logarithmic expression. $$\displaystyle{x}{\ln{\sqrt{{{x}-{4}}}}}$$ Tazmin Horton 2021-11-05 Answered

### Prove the power property of logarithms : $$\displaystyle{{\log}_{{b}}{x}^{{p}}}={p}{{\log}_{{b}}{x}}$$ FobelloE 2021-11-05 Answered

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