Question

Consider the equation 5(10)^(z/4)=32 Solve the equation for z, express the solution as a logarithm in base-10

Answer 1

`\displaystyle z = 4\, \log_(10) \left((32)/(5)\right)`.

Explanation:

Multiply both sides by
`(1/5)` and simplify:

`\displaystyle (1)/(5) * 5\, (10)^(z/4) = (1)/(5) * 32`.

`\displaystyle (10)^(z/4) = (32)/(5)`.

Take the base-
`10` logarithm of both sides:

`\displaystyle \log_(10)\left(10^(z/4)\right) = \log_(10) \left((32)/(5)\right)`.

`\displaystyle (z)/(4) = \log_(10)\left((32)/(5)\right)`.

`\displaystyle z = \log_(10)\left((32)/(5)\right)`.