Using Properties of Logarithms

We will add

1 6^{18}

together and then apply the definition of the logarithm.

1 6^{18} + 2 \cdot 1 6^{18} + 2 \cdot 1 6^{18} = 4^{x}

FactorOutFactor out

1 6^{18}

1 6^{18} (1 + 2 + 2) = 4^{x}

AddTermsAdd terms

1 6^{18} \cdot 5 = 4^{x}

CommutativePropMultCommutative Property of Multiplication

5 \cdot 1 6^{18} = 4^{x}

RearrangeEqnRearrange equation

4^{x} = 5 \cdot 1 6^{18}

Now, let's use the definition of the logarithm.

a^{b} = c 4^{x} = 5 \cdot 1 6^{18} \Leftrightarrow ⇓ \Leftrightarrow b = lo g_{a} c x = lo g_{4} (5 \cdot 1 6^{18})

We can use a calculator to find the value of

x .

x = lo g_{4} (5 \cdot 1 6^{18})

UseCalcUse a calculator

x \approx 37.16096 \dots

RoundDecRound to

x \approx 37.16

Using Properties of Logarithms 1.11 - Solution