Solve 10000=10*2^t/1.5

$$10000 = 10 \times 2 ^ { t / 1.5 }$$

Solve for t

$$t = \frac{9 {(\log_{2} {(5)} + 1)}}{2} \approx 14.948676427$$

Steps Using Definition of Logarithm

Divide both sides by 10.

$$\frac{10000}{10}=2^{\frac{t}{1.5}}$$

Divide 10000 by 10 to get 1000.

$$1000=2^{\frac{t}{1.5}}$$

Swap sides so that all variable terms are on the left hand side.

$$2^{\frac{t}{1.5}}=1000$$

Use the rules of exponents and logarithms to solve the equation.

$$2^{\frac{2}{3}t}=1000$$

Take the logarithm of both sides of the equation.

$$\log(2^{\frac{2}{3}t})=\log(1000)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$\frac{2}{3}t\log(2)=\log(1000)$$

Divide both sides by \log(2).

$$\frac{2}{3}t=\frac{\log(1000)}{\log(2)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$\frac{2}{3}t=\log_{2}\left(1000\right)$$

Divide both sides of the equation by \frac{2}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$t=\frac{3\log_{2}\left(10\right)}{\frac{2}{3}}$$