The functions 𝑗 and 𝑘 are given by          𝑗⁡(𝑥)=log10⁡(𝑥+1)-5⁢log10⁡(2-𝑥)+log10⁡3          𝑘⁡(𝑥)=sec⁡𝑥-cos⁡𝑥.(i) Rewrite 𝑗⁡(𝑥) as a single logarithm base 10 without negative exponents in any part of the expression. Your result should be of the form log10⁡(expression).(ii) Rewrite 𝑘⁡(𝑥) as a product involving tan⁡𝑥 and sin⁡𝑥 and no other trigonometric functions.

The functions 𝑔 and ℎ are given by          𝑔⁡(𝑥)=log5⁡(4⁢𝑥-2)          ℎ⁡(𝑥)=sin-1⁡(8⁢𝑥).(i) Solve 𝑔⁡(𝑥)=3 for values of 𝑥 in the domain of 𝑔.(ii) Solve  ℎ⁡(𝑥)=𝜋4 for values of 𝑥 in the domain of ℎ.

Use the rules of logarithms to write the following expression in terms of ln(𝑥) and ln(𝑦).ln(𝑥3𝑦)=

The properties of logarithms in this section can be used to rewrite log2⁡𝑥5 as follows:𝐴⁢log2⁡𝐵Find the values for 𝐴 and 𝐵:

The function 𝑓 is given by 𝑓⁡(𝑥)=𝑒2⁢𝑥, and the function 𝑔 is given by 𝑔⁡(𝑥)=ln⁡(3⁢𝑥). For 𝑥>0, which of the following is an expression for 𝑓⁡(𝑔⁡(𝑥)) ? Responses9⁢𝑥29 x squared2⁢𝑥+ln⁡32 x plus ln 3(𝑒2⁢𝑥)·ln⁡(3⁢𝑥)open parentheses e to the power of 2 x end exponent close parentheses times ln open parentheses 3 x close parentheses

The functions 𝑔 and ℎ are given by           𝑔⁡(𝑥)=log4⁡(2⁢𝑥)            ℎ⁡(𝑥)=(𝑒𝑥)5𝑒(1/4).(i) Solve 𝑔⁡(𝑥)=3 for values of 𝑥 in the domain of 𝑔.(ii) Solve ℎ⁡(𝑥)=𝑒(1/2) for values of 𝑥 in the domain of ℎ.