Chapter 3

Evaluate the function at the indicated value of x. Round to three decimals.f(x)= 0.9^xx=1.4f(x)=(2/3)^5xx=3/10f(x)=200(1.2)^12xx=24

Evaluate the function at the indicated value of x. Round to three decimals.h(x)=e^-xx=3/4f(x)= 2e^-5xx=10f(x)=5000e^0.006xx=6

Use one-to-one property and solve for x.3^x+1=27(1/2)^x=32e^3x+2=e^3e^(2^x)-3=e^2x

Determine the balance A for P dollars invested at rate r for t years and compounded n time per year. - Compound Interest Formula: A=P((1+(r/n))^(nt)P=$1500, r=2%, t=10 yearsP=$2500, r=4%, t= 20 years

Determine balance A for $12,000 invested at rate r for t years, compounded continuously. Formula: A=Pe^rtr=4%r=6.5%

Write the logarithmic equation in exponential form. log(4)16=2log(9)1/81=-2log(32)4=2/5log(64)8=1/2

Write the exponential equation in logarithmic form.5^3=12581^(1/4)=36^-2= 1/3624^0=1

Evaluate the function at the indicated value of x without using a calculator.f(x)= log(2)xx=64f(x)= log(8)xx=1f(x)=log(a)xx=a^2

Find the domain, x-intercept, and vertical asymptote of the logarithmic function and sketch the graph.f(x)=log(4)xy=-log(3)x+2f(x)=-log(6)(x+2)y=log(x/7)

Write the exponential equation in logarithmic form.e^4=54.598e^1/2=1.6487e^-0.9=0.406e^x=4

Write the logarithmic equation in exponential form. ln(1/2)=-.0693ln7=1.945ln250=5.521ln1=0

Evaluate g(x)=lnx at the indicated value of x without using a calculatorx=e^5x=e^-5/6

Find the domain, x-intercept, and vertical asymptote of the logarithmic function and sketch its graph.f(x)=ln(x-4)g(x)= ln(-x)

Evaluate the logarithm using the change-of-base formula, round to three decimals.log(3)7log(1/2)4log(9)0.1log(15)1250

Use properties of logarithms to rewrite and simplify the logarithmic expression.log(4)8log (5) 1/250ln(5e^6)

Find the exact value without using the calculator.log(3)9log(4)16^2log(2) (-2)

Condense the expression to the logarithm of a single quantity.ln2+lnxlog(4)z-log(4)y2log(2)x+4log(2)y1/4log(3)5xlogx-2log(x+1)logs-2logy+3logzlnx-[ln(x+1)+ln(x-1)]1/3[2ln(x+3)+lnx-ln(x^2-1)]1/3[log(8)y+2log(8)(y+4)]-log(8)(y-1)

Solve the exponential equation algebraically.e^x=e(^x^2)-24(3^x)=202e^x=10e^x-9=193^2x=805^-t/2=0.203^x-1=272^3-x=565