We are given: \(\log_2 (6x + 6) = 5\)

Write in exponential form: \(\log bx=a \to b^a=x\)

\(2^5=6x+6\)

Solve for x: 32=6x+6

26=6x

\(\frac{26}{6}=x\)

or

\(x=\frac{13}{3}\)

asked 2021-05-09

If \(\log_{2} (6x + 6) = 5, \text{then}\ x =?\)

asked 2021-11-08

\(\displaystyle\text{If }\ {y}={\frac{{{3}^{{x}}+{2}}}{{{3}^{{x}}-{2}}}},\ \text{ then }\ {x}={{\log}_{{3}}{\frac{{{2}{y}+{2}}}{{{y}+{k}}}}}\ \text{ for some real number k. What is the value of k? }\ \)

asked 2021-10-29

The One-to-One Property of natural logarithms states that if ln x = ln y, then ________.

asked 2021-11-05

If

\(\displaystyle{{\log}_{{a}}{\left({x}\right)}}={1.5}\)

and \(\displaystyle{{\log}_{{a}}{\left({y}\right)}}={4.7}\)

find the following using the properties of logarithms.

\(\displaystyle{{\log}_{{a}}{\left({\frac{{{x}}}{{{y}}}}\right)}}\)

\(\displaystyle{{\log}_{{a}}{\left({x}\right)}}={1.5}\)

and \(\displaystyle{{\log}_{{a}}{\left({y}\right)}}={4.7}\)

find the following using the properties of logarithms.

\(\displaystyle{{\log}_{{a}}{\left({\frac{{{x}}}{{{y}}}}\right)}}\)

asked 2021-11-09

Write the expression as a single logarithm

\(\displaystyle{6}{{\log}_{{5}}{\left({x}-{3}\right)}}-{4}{{\log}_{{5}}{\left({x}+{4}\right)}}\)

\(\displaystyle{6}{{\log}_{{5}}{\left({x}-{3}\right)}}-{4}{{\log}_{{5}}{\left({x}+{4}\right)}}\)

asked 2021-11-10

Solve for xx.

\(\displaystyle{{\log}_{{2}}{\left({x}\right)}}+{{\log}_{{2}}{\left({x}−{12}\right)}}={6}\)

\(\displaystyle{{\log}_{{2}}{\left({x}\right)}}+{{\log}_{{2}}{\left({x}−{12}\right)}}={6}\)

asked 2021-10-29

Solve: \(\displaystyle{\ln{{\left({x}\right)}}}={\ln{{\left({x}+{6}\right)}}}-{\ln{{\left({x}-{4}\right)}}}\)