Surds and Indices Quiz Set 004

We can write the given expression as $3^x = 3^3$. The bases are same so powers should be same. Comparing we get x = 3.

We can simplify the given expression to $26^{0.24 + x} = 26^0.15$. The bases are equal, so the powers should also be equal. Hence $0.24 + x = 0.15$ which gives x = -0.09.

By inspection, we get $(2^4)^0.15 × (2^4)^0.1$, which equals $(2^4)^(0.15 + 0.1)$, which equals $(2^4)^0.25$, which equals $2^1$, or 2. Note: The trick in such type of questions is to keep an eye on the "bases".

We can write the given expression as $6^x = 6^2$. The bases are same so powers should be same. Comparing we get x = 2.

We can simplify the given expression to $({19/28})^{0.12 + x} = ({19/28})^0.11$. The bases are equal, so the powers should also be equal. Hence $0.12 + x = 0.11$ which gives x = -0.00999999999999998.