What is the answer to log_{a}(2)+2log_{a}(7)=2 ?

The answer to log_{a}(2)+2log_{a}(7)=2 is a=e^{(ln(98))/2}

Solve for a: log_{a}(2)+2log_{a}(7)=2

The solution is a=e^{(ln(98))/2}

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lo g_{a} (2) + 2 lo g_{a} (7) = 2

a = e^{\frac{l n ( 98 )}{2}}

Decimal Notation

a = 9.89949 \dots

Solution steps

lo g_{a} (2) + 2 lo g_{a} (7) = 2

Apply log rules

\frac{ln ( 2 \cdot 7 ^{2} )}{ln ( a )} = 2

Multiply both sides by

ln (a)

\frac{ln ( 2 \cdot 7 ^{2} )}{ln ( a )} ln (a) = 2 ln (a)

Simplify

ln (98) = 2 ln (a)

Switch sides

2 ln (a) = ln (98)

Divide both sides by

2

ln (a) = \frac{ln ( 98 )}{2}

Apply log rules

a = e^{\frac{l n ( 98 )}{2}}

Verify Solutions:

a = e^{\frac{l n ( 98 )}{2}}

True

The solution is

a = e^{\frac{l n ( 98 )}{2}}

0.5 = - lo g_{10} (t)

ln (x + 4) + ln (x + 5) = 1

ln (8 - 8 x) = - 3

4 lo g_{10} (x) = 10

lo g_{10} (z + j) = 0

What is the answer to log_{a}(2)+2log_{a}(7)=2 ?
The answer to log_{a}(2)+2log_{a}(7)=2 is a=e^{(ln(98))/2}
Solve for a: log_{a}(2)+2log_{a}(7)=2
The solution is a=e^{(ln(98))/2}