Question

102,672 = 54,066 (0.03)^x

Answer 1

x = -0.1829

Explanation:

102,672 = 54,066 (0.03)^x

Divide both sides by 54066.

102672/54066 = (0.03)^x

1.899 = 0.03^x

Since the x is in the exponent, you can take the log of both sides, OR change from exponential form to logarithmic form.

One Way:

log 1.899 = log.03^x

log 1.899 = xlog.03

Divide both sides by log.03

(log1.899)/log.03 = x

-0.18289557 = x

x = -0.1829

OR the other way:

1.899 = 0.03^x

Change to logarithmic form.

log_.03 (1.899) = x

Use Change of Base formula (or a high speed calculator)

log(1.899)/log(.03)=x

-0.1829 = x

Answer 2

x ≈ -0.18289557

Explanation:

Given the equation 102,672 = 54,066 (0.03)^x, you want the value of x.

Solution

Divide by 54,066 to get ...

(102672/54066) = 0.03^x

Take logarithms, and you have ...

log(102672/54066) = x·log(0.03)

Dividing by the coefficient of x gives you ...

x = log(102672/54066)/log(0.03) ≈ -0.18289557