Question

what steps would I use to solve the equation
1.8=(1.05)(power of X)

Answer 1

Take the ln of both sides first and you will be able to apply log rules:
\[ln(1.8)=ln(1.05^x)\]
Per the log rule:
\[ln(m^n)=nln(m)\]
\[ln(1.8)=xln(1.05)\]
\[x=\frac{ln1.8}{ln1.05}\]
\[x=12.05\]

Answer 2

Logarithms!!!
log(1.8) = xlog(1.5)
divide both side by log(1.5)
x = 12.0472

Answer 3

Alternatively you can also use log instead of ln.

Answer 4

log = log base 10
ln = log base e
use the change of base formulas to convert.
log base x of y = log(y)/log(x)