Answer
$5*1.06^{2x+1}=11$
$1.06^{2x+1}=\frac{11}{5}=2.2$
$\log_{1.06}2.2=2x+1$
$\log_{1.06}2.2-1=2x$
$\frac{\log_{1.06}2.2-1}{2}=x$
$\frac{12.5314}{2}=x$
$6.2657=x$
Work Step by Step
The definition of the logarithm function can be translated into mathematical formulas such as the following. The given expressions are equivalent.
The exponential form: $b^{x}=a$
The logarithmic form: $\log_{b}a=x$.
The given equation can be solved with the logarithmic form, therefore we shall transform it:
$5*1.06^{2x+1}=11$
$1.06^{2x+1}=\frac{11}{5}=2.2$
$\log_{1.06}2.2=2x+1$
$\log_{1.06}2.2-1=2x$
$\frac{\log_{1.06}2.2-1}{2}=x$
$\frac{12.5314}{2}=x$
$6.2657=x$
