Provide an appropriate response: Write the algebraic equation which can be used to find the exact solution of log lower case 2 to (x+8) +log lower case 2 to (x+8)=4

Solve the problem:

1. Suppose that y=2-log (100-x)/0.27 can be used to calculate the number of years y for x percent of a population of 257 web-footed sparrows to die. Approximate the percentage (to the nearest whole per cent) of web-footed sparrows that died after 4 yr.

2. A sample of 450 grams of radioactive substance decays according to the function A(t)=450e^-.025t, where t is the time in years. How much of the substance will be left in the sample after 40 years? Round your answer to the nearest whole gram.

3. Suppose the government wants to impose a tax on fossil fuels to reduce carbon emissions. The cost benefit is modeled by in(1-P)=-0.0031-0.0048x, where x represents the dollars of tax per ton of carbon emitted and P represents the percent reduction in emissions of carbon. (P is in decimal form.) Determine P when x=67. Round to three decimal places.

4. Use the properties of logarithms to rewrite the logarithm if possible. Assume that all variables represent positive real numbers: log lower case 4 to x^4 y^8/3

Graph the function: f(x)=1/3^x+2