4.8 Fitting exponential models to data  (Page 10/12)

The graph below shows transformations of the graph of $f(x)=2^x.$ What is the equation for the transformation?

Rewrite ${\log }_{17}\left(4913\right)=x$ as an equivalent exponential equation.

Rewrite $\ln \left(s\right)=t$ as an equivalent exponential equation.

Rewrite $a^{-\frac{2}{5}}=b$ as an equivalent logarithmic equation.

Rewrite $e^{-3.5}=h$ as an equivalent logarithmic equation.

Solve for $x{\log }_{64}(x)=\frac{1}{3}$ to exponential form.

Evaluate ${\log }_5\left(\frac{1}{125}\right)$ without using a calculator.

Evaluate $\log \left(\text{0}\text{.000001}\right)$ without using a calculator.

Evaluate $\log (4.005)$ using a calculator. Round to the nearest thousandth.

Evaluate $\ln \left(e^{-0.8648}\right)$ without using a calculator.

Evaluate $\ln \left(\sqrt[3]{18}\right)$ using a calculator. Round to the nearest thousandth.

Graph the function $g(x)=\log \left(7x+21\right)-4.$

Graph the function $h(x)=2\ln \left(9-3x\right)+1.$

State the domain, vertical asymptote, and end behavior of the function $g(x)=\ln \left(4x+20\right)-17.$

Rewrite $\ln \left(7r\cdot 11st\right)$ in expanded form.

Rewrite ${\log }_8\left(x\right)+{\log }_8\left(5\right)+{\log }_8\left(y\right)+{\log }_8\left(13\right)$ in compact form.

Rewrite ${\log }_m\left(\frac{67}{83}\right)$ in expanded form.

Rewrite $\ln \left(z\right)-\ln \left(x\right)-\ln \left(y\right)$ in compact form.

Rewrite $\ln \left(\frac{1}{x^5}\right)$ as a product.

Rewrite $-{\log }_y\left(\frac{1}{12}\right)$ as a single logarithm.

Use properties of logarithms to expand $\log \left(\frac{r^2{s}^{11}}{t^{14}}\right).$

Use properties of logarithms to expand $\ln \left(2b\sqrt{\frac{b+1}{b-1}}\right).$

Condense the expression $5\ln \left(b\right)+\ln \left(c\right)+\frac{\ln \left(4-a\right)}{2}$ to a single logarithm.

Condense the expression $3{\log }_{7}v+6{\log }_{7}w-\frac{{\log }_{7}u}{3}$ to a single logarithm.

Rewrite ${\log }_3\left(12.75\right)$ to base $e.$

Rewrite $5^{12x-17}=125$ as a logarithm. Then apply the change of base formula to solve for $x$ using the common log. Round to the nearest thousandth.

Solve ${216}^{3x}\cdot {216}^x={36}^{3x+2}$ by rewriting each side with a common base.

Solve $\frac{125}{{\left(\frac{1}{625}\right)}^{-x-3}}=5^3$ by rewriting each side with a common base.

Use logarithms to find the exact solution for $7\cdot {17}^{-9x}-7=49.$ If there is no solution, write no solution .

Use logarithms to find the exact solution for $3e^{6n-2}+1=-60.$ If there is no solution, write no solution .

Find the exact solution for $5e^{3x}-4=6$ . If there is no solution, write no solution .

Find the exact solution for $2e^{5x-2}-9=-56.$ If there is no solution, write no solution .

Find the exact solution for $5^{2x-3}=7^{x+1}.$ If there is no solution, write no solution .

Find the exact solution for $e^{2x}-e^x-110=0.$ If there is no solution, write no solution .

Use the definition of a logarithm to solve. $-5{\log }_7\left(10n\right)=5.$

47. Use the definition of a logarithm to find the exact solution for $9+6\ln \left(a+3\right)=33.$

Use the one-to-one property of logarithms to find an exact solution for ${\log }_8\left(7\right)+{\log }_8\left(-4x\right)={\log }_8\left(5\right).$ If there is no solution, write no solution .

Use the one-to-one property of logarithms to find an exact solution for $\ln \left(5\right)+\ln \left(5x^2-5\right)=\ln \left(56\right).$ If there is no solution, write no solution .

The formula for measuring sound intensity in decibels $D$ is defined by the equation $D=10\log \left(\frac{I}{I_0}\right),$ where $I$ is the intensity of the sound in watts per square meter and $I_0={10}^{-12}$ is the lowest level of sound that the average person can hear. How many decibels are emitted from a large orchestra with a sound intensity of $6.3\cdot {10}^{-3}$ watts per square meter?