solve the exponential equation algebraically: 4^-3t = 0.10

Answer 1

4^-3t = 10^-1

log 4^-3t = log 10^-1

-3t log 4 = -1

t = 1 / (3 log 4)

Answer 2

4^-3t = 0.10

You can rewrite 4^-3t as 1/4^3t and 0.10 as 1/10.

So the equation can be rewritten as:

1/4^3t = 1/10

Multiply both sides by 10

10 x 1/4^3t = 10 x 1/10

Simplify

10/4^3t = 1

Multiply both sides by 4^3t

₄^3t x 10/4^{3t =} 4^3t x 1

Simplify

10 = 4^3t

Use the power rule of exponents to rewrite 4^3t

10 = (4³)^t

Multiply out the exponential expression by multiplying 4x4x4 in the parentheses

10 = 64^t

Write the equation in logarithmic formal get the answer for t

t = log₆₄10