Solve for x. 15.7(0.98)^x = 11(0.99)^x

Answer 1

Let's divide both sides by 0.99^x and by 15.7

We'll get (0.98/0.99)^x = 11/15.7

Taking LN on both sides: ln( (0.98/0.99)^x ) = ln(11/15.7)

Applying laws of logarithms: x(ln0.98 - ln0.99) = ln11 - ln15.7

x = (ln11 - ln15.7) / (ln0.98 - ln0.99)

Answer 2

15.7(0.98)^x = 11(0.99)^x

Remember the rules of logarithms. We want to take the natural log of both sides.

ln(15.7(0.98)^x) = ln(11(0.99)^x)

If you have multiplication inside the logarithm, it can be rewritten as the addition of two logs.

ln(15.7)+ln((0.98)^x) = ln(11)+ln((0.99)^x)

Next, if you have an exponent in the logarithm, it can be brought in front of the log to multiply it.

ln(15.7)+xln(0.98) = ln(11)+xln(0.99)

Now all we need to do is combine like terms and simplify.

ln(15.7)-ln(11)= xln(0.99)-xln(0.98)

ln(15.7)-ln(11)= x(ln(0.99)-ln(0.98))

X = (ln(15.7)-ln(11)) / (ln(0.99)-ln(0.98))