# Recent questions tagged exponents

121
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Compute, if possible, the limits: $$\lim _{x \rightarrow 0} \sin (x)$$ and $$\lim _{x \rightarrow 0} \sin (1 / x)$$
80
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Evaluate the following limit.$\lim _{x \rightarrow \infty} x^{\frac{1}{x}}$
84
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Evaluate $$\lim_{x \to 0} \left(\frac{\sin(x)}{x}\right)$$
108
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Evaluate $\lim_{x \to \infty} \left(\frac{2x^2 - 3x + 1}{5x^2 + 2x - 1}\right)$
97
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Evaluate $$\lim_{x \to 2} \left(\frac{x^2 - 4}{x - 2}\right)$$
66
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Evaluate $$\lim_{x \to 2} (3x + 4)$$
96
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Find $$\lim _{x \rightarrow \pm \infty} \frac{7 x^{3}+2 x^{2}}{4 x^{3}-x}$$.
128
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Evaluate $$\lim _{x \rightarrow 4^{+}} \frac{3}{x-4}$$ and $$\lim _{x \rightarrow 4^{-}} \frac{3}{x-4}$$
89
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Find $$\lim _{x \rightarrow 0^{+}} \frac{|x|}{x}$$ and $$\lim _{x \rightarrow 0^{-}} \frac{|x|}{x}$$.
84
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Is $$\log_{10}2$$ rational?
64
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Solve: $$\sqrt{\ln x}=\ln (\sqrt{x})$$.
57
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Find the derivative of the given function:$y=\ln (\ln x)$
66
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Solve $$\ln _{2}(x+1)-\ln _{2}(x-1)=\ln _{2} 8$$
66
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Solve $$\ln _{3} x=5$$
164
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Is the number $$-\frac{10}{3}$$ a rational number?
127
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Evaluate the limit$\lim _{x \rightarrow 0} \frac{x^{2}-25}{x^{2}-4 x-5}$
552
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What is the power rule for differentiation?
208
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Simplify $$\frac{3^{2 x} \cdot 27^{x-1}}{9^{2 x+2}}$$
274
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Write down the six laws for exponents. Use latex
367
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Convert $$\sqrt{49}=7$$ into a logarithmic equation.
226
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Convert $$10^{-3}=\frac{1}{1,000}$$ into a logarithmic equation.
213
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Rewrite $$5^3=125$$ as a logarithmic equation.
383
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Convert $$\log _3\left(\frac{1}{81}\right)=-4$$ into an exponential equation.
231
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Convert $$\log _4\left(\frac{1}{16}\right)=-2$$ into an exponential equation.
550
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Rewrite $$\log _3 9=2$$ as an exponential equation.
213
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Evaluate. $$x^3$$ if $$x=-4$$
267
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Evaluate. $$(5 x)^3$$ if $$x=4$$
568
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What is a rational number?
258
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Solve for $$x$$ $4 x^2-4 x-1=0$ (leave your answers in simplest surd form)
336
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How do you simplify an expression with exponents?
255
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Simplify the following:(a) $$\dfrac{\cos \left(180^{\circ}-\theta\right) \cdot \cos \left(90^{\circ}-\theta\right)}{\sin \left(90^{\circ}+\theta\right) \cdot \sin \left(-... 318 views 1 answers Simplify the following using the laws of logarithms:(a) \(\quad \log _9 27$$(b) $$\quad \log _3 2 \cdot \log _2 5 \cdot \log _5 9$$
264
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Prove that $$\log _a x=\frac{\log _b x}{\log _b a}$$
273
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simplify $$\log _3 \sqrt{27}$$
308
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Simplify $$\log _3 \frac{1}{27}$$
283
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simplify $$-\log 4-\log 25$$
578
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simplify $$\log 20+\log 30-\log 6+\log _4 1$$
337
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Simplify using laws of logs $$\log _3 27-\log _3 3$$
257
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Simplify $$\log _9 27+\log _9 3$$
486
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Prove that $$\log _a a=1$$
288
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Using the laws of logarithms, expand $$\log _4\left(\frac{5}{x}\right)$$
198
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Expand $$\log_{3}5x$$
282
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Prove that $$\log _a x^m=m \log _a x \quad(x>0, y>0,0<a<1$$ or $$a>1)$$
398
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Prove that $$\log _a\left(\frac{x}{y}\right)=\log _a x-\log _a y \quad(x>0, y>0,0<a<1$$ or $$a>1)$$
315
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Prove that $$\log _a(x \times y)=\log _a x+\log _a y \quad(x>0, y>0,0<a<1$$ or $$a>1)$$
424
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Find the derivative of the function $f(x) = x^3 + 3x^2 - 7x + 2$.
398
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Find the derivative of the function $f(x) = \ln x$
Find the derivative of the function $f(x) = x^3 + 2x^2 + 3x + 4$